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Trigonometry Tutorial
by Superjoe Software
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Superjoe
Software

Trigonometry is sometimes confusing,
but if you look in to it a little bit, Trig is
very helpful and worth the extra bit of
work it takes to implement.

Continue

Why Use Trig?

Trig Tutorial by Superjoe Software

Previous Step

Next Step

You can create interesting effects using Trigonometry.
All of these cool effects I created using Trig.

The arrow points at
the cursor.

The fish points in the
direction he swims.

The clock hands
point to the correct
numbers.

If you're still not convinced, you should know that you
have to use Trig in a lot of games, to make bullets
point in the direction they are fired, to make a
helicopter point up a little bit when it rises, and so on.
Plus, you'll probably have to learn it in Math class
anyways.

Trigonometry has to do with circles, angles,
and triangles.

A circle is broken down into 4 quadrants.

III

Trig Overview

An angle is a specific amount that specifies
a rotation. To show this rotation, we use
degrees (°). 0° means no rotation, and 360°
means rotated so far that it is rotated back to
the beginning.

The blue line
marks 0° and
360°.

Watch as the red line rotates. The number
shows you what angle the red line makes
with the blue line.

0°

The basics of Trigonometry is the fact that if
you know a few things about a triangle, you
can figure out everything else.

The triangle must be a right triangle,
meaning that one of its angles is 90°.

This angle is
90 degrees

Getting Into Mathematics

We'll name the sides of our triangle x, y, and r.
We only need to name one of the angles.
We'll call it theta (ø).

With a triangle set up this way, all you need is
2 of the 4 variables in the drawing, and you
can find the other 2 using Trig. To do this, use
these equations.

r^2 = x^2 + y^2sin(ø) = y / rcos(ø) = x / rtan(ø) = y / x

Note that you will have to
solve the equation for the
variable you wish to use.

sin(), cos(), and tan() are handy trig functions. You
access them in flash by using Math.sin(),
Math.cos(), and Math.tan(). However, these
functions may not act like you expect them to if
you supply angle arguments in degrees. These
functions use a different measuring system:
radians.

Radians is the same thing as degrees, but instead
of going from 0° to 360°, radians go from 0 to 2 * π.
π is a mathematical constant approximately equal
to 3.14. It is accessible in Flash using Math.PI.

0°

90°

180°

315°

270°

45°

135°

225°

π/2

7/4 * π

3/2 * π

π/4

3/4 * π

5/4 * π

It is easy to convert between degrees and radians.
To do so, use these equations:

radians = (degrees * π) / 180degrees = (180 * radians) / π

Important!
Take note that Flash uses degrees, but using Trig
functions in Flash requires that you use radians.

Let's look at the arrow again.

When you create a symbol in Flash, the
registration point is the point of rotation. For the
arrow, I placed it in the center. All we have to do is
make the arrow rotate to face the cursor point.

Explaining the Demos - Rotating Arrow

Are you seeing the triangle?

Theta (ø) is the angle we need to find. We can get
x and y by subtracting the x and y locations of the
arrow from the x and y locations of the mouse.

x = Math.abs(_root._xmouse - mc_arrow._x);y = Math.abs(_root._ymouse - mc_arrow._y);

Now that know x and y, we can find theta.
Remember the equations?

The equation we need for this one is
tan(ø) = y / x
But we have a problem. We can't just enter that
into a line of code. We have to solve for theta (ø).

This is done by taking the arc tangent of both sides:
ø = atan(y / x)

Now all we have to do is convert theta (ø) to
degrees and set the arrow's rotation. Assuming the
name of the movie clip is "mc_arrow," this code will
rotate it:

mc_arrow

mc_arrow._rotation = (180 * theta) / Math.PI;

This works great - until the mouse exits the first
quadrant. Remember the quadrant circle?

We have to make a separate triangle
for each quadrant.

0°

Remember that rotation starts from the 0° position.
Theta (ø) is just an angle of a triangle.

Once you find theta, there's a little bit more to it
than converting to degrees. Rotation is absolute;
theta is relative. You have to make a different
reference point for each quadrant.

III

To overcome this challenge, we'll write code to
handle the 4 different quadrants:

if(_xmouse >= mc_arrow._x && _ymouse <= mc_arrow._y){  //quadrant I  mc_arrow._rotation = (180*theta)/Math.PI;}else if(_xmouse < mc_arrow._x && _ymouse <= mc_arrow._y){  //quadrant II  mc_arrow._rotation = 180 - (180*theta)/Math.PI;}else if(_xmouse >= mc_arrow._x && _ymouse > mc_arrow._y){  //quadrant III  mc_arrow._rotation = 180 + (180*theta)/Math.PI;}else {  //quadrant IV  mc_arrow._rotation = 360 - (180*theta)/Math.PI;}

All this does is start the rotation at 0°.

Only one last thing stands before you and a
finished rotating arrow Flash. It is this simple fact:
Mathematics rotates counter-clockwise, while
Flash MX rotates clockwise.
This is an easy challenge to overcome. All you
have to do is slap a negative sign (-) in front of the
angle you specify for the _rotation property.
Click here if you want to see the full source code
listing for the rotating arrow. It may look different
than what I've shown you so far, because I made
the code more efficient.

Rotating Arrow Code Listing

this.onEnterFrame = function(){  xdist = Math.abs(_root._xmouse - mc_arrow._x);  ydist = Math.abs(_root._ymouse - mc_arrow._y);  theta = Math.atan(ydist/xdist);  if(_root._xmouse >= mc_arrow._x && _root._ymouse <= <sbr />mc_arrow._y){    angle = theta;  }else if(_root._xmouse < mc_arrow._x && _root._ymouse <sbr /><= mc_arrow._y){    angle = Math.PI - theta;  }else if(_root._xmouse < mc_arrow._x && _root._ymouse > <sbr />mc_arrow._y){    angle = Math.PI + theta;  }else {    angle = (2 * Math.PI) - theta;  }  mc_arrow._rotation = -((180*angle) / Math.PI);}

On to the next Trig demo! This is the code I added
for the ABS Fishtank. I made it so that the fish
point in the direction they swim. Let's watch the
fishy again.

Explaining the Demos - Swimming Fish

The movement of the fish is not particularly
beautiful, but it gets my Trigonometry point across.
I'm not going to explain all the code, just the Trig
part. Basically, the fish picks a target location
randomly within the box. The code uses Trig to
point the fish in the right direction, and then the fish
swims until it reaches its destination, starting the
process over again.

The fish is just sitting there, and then it decides a
target point. It needs to rotate to point at the target.

Are you seeing the triangle?

Target

You should know how to do the rest of it from the
arrow demo, but in case you forgot already, I'll walk
you through it again real quick.

1. Find x and y using x = targetX - fish._x;
and y = targetY - fish._y;

2. Find theta using theta = Math.atan(y / x);

3. Edit your code so it works with all 4 quadrants.

III

In this case we have a problem.
Unlike the arrow, the fish is not
symmetrical. This means that
when the fish is rotated so that it
is facing left, it would be upside
down.

To correct this, place the fish inside a movie clip. In
the first frame, make the fish face right. In the second
frame, make the fish face left. Then, in your code,
adjust the direction of the fish by using
fish.gotoAndStop([1 or 2]);

In quadrants 1 and 4, make the fish point right.
In quadrants 2 and 3, make the fish point left.

The final thing you need to do is adjust theta. Because
the fish facing left starts at 180°, and not 0°, you have
to subtract 180° from theta in quadrants 2 and 3.

4. When you finally set the _rotation property,
negate the angle.

Obviously, there's more to the code for the fish than
Trigonometry. The code I created for moving the fish
around is poorly coded and not very good, but the
code for setting the correct rotation is superb, so that's
what you should pay attention to.
Click here to see the full source listing for the
swimming fish.

Swimming Fish Code Listing

curTime = 0;targX = 0;targY = 0;fishSpd = 4;fishSwimming = false;xT = false;yT = false;this.onEnterFrame = function(){  if(!fishSwimming && getTimer() - curTime > 1000){    fishSwimming = true;    targX = tank._x + Math.random() * tank._width;    targY = tank._y + Math.random() * tank._height;    //point the fish    xdist = Math.abs(targX - fish._x);    ydist = Math.abs(targY - fish._y);    theta = Math.atan(ydist/xdist);    if(_root.targX >= fish._x && targY <= fish._y){      angle = theta;      fish.gotoAndStop(1);    }else if(targX < fish._x && targY <= fish._y){      angle = - theta;      fish.gotoAndStop(2);    }else if(targX < fish._x && targY > fish._y){      angle =  theta;      fish.gotoAndStop(2);    }else {      angle = (2 * Math.PI) - theta;      fish.gotoAndStop(1);    }    fish._rotation = -((180*angle) / Math.PI);  }  if(fishSwimming){    if(fish._x <= targX){      if(fish._x+ fishSpd >= targX){        fish._x = targX;        xT = true;      }else{        fish._x += fishSpd;      }    } else if(fish._x >= targX) {    if(fish._x- fishSpd <= targX){      fish._x = targX;      xT = true;    }else{     fish._x -= fishSpd;    }  }  if(fish._y <= targY){    if(fish._y+ fishSpd >= targY){      fish._y = targY;      yT = true;    }else{      fish._y += fishSpd;    }  } else if(fish._y >= targY) {    if(fish._y- fishSpd <= targY){        fish._y = targY;        yT = true;      }else{        fish._y -= fishSpd;      }    }    if(xT && yT){      fishSwimming = false;      curTime = getTimer();      xT = false;      yT = false;          }  }}

This example really doesn't have too much to do with
Trig, but I put it in because it has to do with circles,
angles, and rotation. The point is, if you're good at
Trig, using the _rotation property is a cinch. Let's
see what time it is.

Hmm, it's been 1 hours, 32 minutes, and 56 seconds since you looked at this clock.

Explaining the Demos - Clock

The first thing you have to do is create the clock
outline. I did a nice, simple one using the circle tool
and the text tool.

Next, I created the hands. Instead of making them
point right, like I usually do, I made them point up,
because that's where the clock starts.

The important thing when making the hands is to set
the registration point at the bottom. That way, when
you rotate the hands, they rotate around the clock.

Next, I simply positioned the registration point at the
center of the clock. When we rotate it, the clock hands
will act like they are supposed to.

Now we come to the easy, fun part. We'll put some
ActionScript in the frame with the clock. The code for
retrieving the current time in Flash is:
curTime = new Date();
That's all. The variable curTime now holds the
current date and time. To extract hours, minutes, and
seconds, use:
hours = curTime.getHours();
minutes = curTime.getMinutes();
seconds = curTime.getSeconds();

Unforunately, I can't ask you if you're seeing the
triangle, because there isn't one. All you have to do is
make a proportion. Flash rotates clockwise, so all you
have to do is decide how far to rotate. Well, the
maximum amount of minutes is 60, so that ones easy:

minuteHand._rotation = (curTime.getMinutes() / 60) * 360;

And it's the same thing with the second hand:

secondHand._rotation = (curTime.getSeconds() / 60) * 360;

The only problem arises with the hour hand. When
you use curTime.getHours(), it returns the hours
in 24-hour time format. Three simple lines of code will
overcome that:

hours = nowTime.getHours();if (hours > 12) hours -= 12;hourHand._rotation = (hours / 12) * 360;

You should be able to create a working clock now.
That example was pretty easy.
Click here to see the full source code listing for the
clock. It's not very much code at all.

Clock Code Listing

If you were paying attention, you should be able to
use trig to assist your animations and games.
Keep your chin up - Trig can get complicated. If
something is not going as expected, mess around with
theta. Try making it negative, or adding/subtracting
180°, or anything you can think of. Usually, it takes me
4 or 5 tries until my Trig code works out. Even when I
was making this tutorial, the Trig didn't work out right
at first. Keep trying and you'll get it eventually.

Congratulations

Congratulations, you just spent 5 hours, 56 minutes, and 23 seconds learning about Trigonometry. You should ask your teacher for extra credit or something.

Made for <a href="http://www.albinoblacksheep.com">Albino Blacksheep</a>

by<a href="http://www.geocities.com/joesarcade">Superjoe Software</a>

ActionScript [AS1/AS2]

Frame 1
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		System.security.allowDomain("mochibot.com");
	}
	_level0.__com_mochibot__swfid = "47e14f78";
	loadMovieNum ("http://mochibot.com/my/core.swf", 10301);

	loadPercent = _root.getBytesLoaded() / _root.getBytesTotal();
	degrees = loadPercent * 360;
	ticker._rotation = degrees;
Frame 2
	if (_root.getBytesLoaded() < _root.getBytesTotal()) {
		gotoAndPlay (1);
	}
Frame 3
	stop();
Frame 21
	stop();
Frame 22
	curTime = 0;
	targX = 0;
	targY = 0;
	fishSpd = 4;
	fishSwimming = false;
	xT = false;
	yT = false;
	onEnterFrame = function () {
		xdist = Math.abs(_root._xmouse - mc_arrow._x);
		ydist = Math.abs(_root._ymouse - mc_arrow._y);
		theta = Math.atan(ydist / xdist);
		if ((_root._xmouse >= mc_arrow._x) && (_root._ymouse <= mc_arrow._y)) {
			angle = theta;
		} else if ((_root._xmouse < mc_arrow._x) && (_root._ymouse <= mc_arrow._y)) {
			angle = Math.PI - theta;
		} else if ((_root._xmouse < mc_arrow._x) && (_root._ymouse > mc_arrow._y)) {
			angle = Math.PI + theta;
		} else {
			angle = (Math.PI*2) - theta;
		}
		mc_arrow._rotation = -((180 * angle) / Math.PI);
		if ((!fishSwimming) && ((getTimer() - curTime) > 1000)) {
			fishSwimming = true;
			targX = tank._x + (Math.random() * tank._width);
			targY = tank._y + (Math.random() * tank._height);
			xdist = Math.abs(targX - fish._x);
			ydist = Math.abs(targY - fish._y);
			theta = Math.atan(ydist / xdist);
			if ((_root.targX >= fish._x) && (targY <= fish._y)) {
				angle = theta;
				fish.gotoAndStop(1);
			} else if ((targX < fish._x) && (targY <= fish._y)) {
				angle = -theta;
				fish.gotoAndStop(2);
			} else if ((targX < fish._x) && (targY > fish._y)) {
				angle = theta;
				fish.gotoAndStop(2);
			} else {
				angle = (Math.PI*2) - theta;
				fish.gotoAndStop(1);
			}
			fish._rotation = -((180 * angle) / Math.PI);
		}
		if (fishSwimming) {
			if (fish._x <= targX) {
				if ((fish._x + fishSpd) >= targX) {
					fish._x = targX;
					xT = true;
				} else {
					fish._x = fish._x + fishSpd;
				}
			} else if (fish._x >= targX) {
				if ((fish._x - fishSpd) <= targX) {
					fish._x = targX;
					xT = true;
				} else {
					fish._x = fish._x - fishSpd;
				}
			}
			if (fish._y <= targY) {
				if ((fish._y + fishSpd) >= targY) {
					fish._y = targY;
					yT = true;
				} else {
					fish._y = fish._y + fishSpd;
				}
			} else if (fish._y >= targY) {
				if ((fish._y - fishSpd) <= targY) {
					fish._y = targY;
					yT = true;
				} else {
					fish._y = fish._y - fishSpd;
				}
			}
			if (xT && (yT)) {
				fishSwimming = false;
				curTime = getTimer();
				xT = false;
				yT = false;
			}
		}
		nowTime = new Date();
		hours = nowTime.getHours();
		if (hours > 12) {
			hours = hours - 12;
		}
		hourH._rotation = (hours / 12) * 360;
		minH._rotation = (nowTime.getMinutes() / 60) * 360;
		secH._rotation = (nowTime.getSeconds() / 60) * 360;
		clockTime = getTimer();
	};
Frame 26
	rot = 0;
	wid = redLine._width;
	this.onEnterFrame = function () {
		rot++;
		if (rot > 360) {
			rot = rot - 360;
		}
		redLine._rotation = -rot;
		degClip._x = redLine._x + (wid * Math.cos(((-rot) * Math.PI) / 180));
		degClip._y = redLine._y + (wid * Math.sin(((-rot) * Math.PI) / 180));
		degClip.numDegrees.text = rot + "\u00B0";
	};
Frame 34
	onEnterFrame = function () {
		xdist = Math.abs(_root._xmouse - mc_arrow._x);
		ydist = Math.abs(_root._ymouse - mc_arrow._y);
		theta = Math.atan(ydist / xdist);
		if ((_root._xmouse >= mc_arrow._x) && (_root._ymouse <= mc_arrow._y)) {
			angle = theta;
		} else if ((_root._xmouse < mc_arrow._x) && (_root._ymouse <= mc_arrow._y)) {
			angle = Math.PI - theta;
		} else if ((_root._xmouse < mc_arrow._x) && (_root._ymouse > mc_arrow._y)) {
			angle = Math.PI + theta;
		} else {
			angle = (Math.PI*2) - theta;
		}
		mc_arrow._rotation = -((180 * angle) / Math.PI);
	};
Frame 43
	arrowCode._visible = false;
Frame 44
	curTime = 0;
	targX = 0;
	targY = 0;
	fishSpd = 4;
	fishSwimming = false;
	xT = false;
	yT = false;
	this.onEnterFrame = function () {
		if ((!fishSwimming) && ((getTimer() - curTime) > 1000)) {
			fishSwimming = true;
			targX = tank._x + (Math.random() * tank._width);
			targY = tank._y + (Math.random() * tank._height);
			xdist = Math.abs(targX - fish._x);
			ydist = Math.abs(targY - fish._y);
			theta = Math.atan(ydist / xdist);
			if ((_root.targX >= fish._x) && (targY <= fish._y)) {
				angle = theta;
				fish.gotoAndStop(1);
			} else if ((targX < fish._x) && (targY <= fish._y)) {
				angle = -theta;
				fish.gotoAndStop(2);
			} else if ((targX < fish._x) && (targY > fish._y)) {
				angle = theta;
				fish.gotoAndStop(2);
			} else {
				angle = (Math.PI*2) - theta;
				fish.gotoAndStop(1);
			}
			fish._rotation = -((180 * angle) / Math.PI);
		}
		if (fishSwimming) {
			if (fish._x <= targX) {
				if ((fish._x + fishSpd) >= targX) {
					fish._x = targX;
					xT = true;
				} else {
					fish._x = fish._x + fishSpd;
				}
			} else if (fish._x >= targX) {
				if ((fish._x - fishSpd) <= targX) {
					fish._x = targX;
					xT = true;
				} else {
					fish._x = fish._x - fishSpd;
				}
			}
			if (fish._y <= targY) {
				if ((fish._y + fishSpd) >= targY) {
					fish._y = targY;
					yT = true;
				} else {
					fish._y = fish._y + fishSpd;
				}
			} else if (fish._y >= targY) {
				if ((fish._y - fishSpd) <= targY) {
					fish._y = targY;
					yT = true;
				} else {
					fish._y = fish._y - fishSpd;
				}
			}
			if (xT && (yT)) {
				fishSwimming = false;
				curTime = getTimer();
				xT = false;
				yT = false;
			}
		}
	};
Frame 53
	fishCode._visible = false;
Frame 54
	secondsPassed = Math.floor((getTimer() - clockTime) / 1000);
	if (secondsPassed >= 60) {
		minutesPassed = Math.floor(secondsPassed / 60);
		secondsPassed = secondsPassed % 60;
		if (minutesPassed >= 60) {
			hoursPassed = Math.floor(minutesPassed / 60);
			minutesPassed = minutesPassed % 60;
		}
	}
	newText = "Hmm, it's been";
	if (hoursPassed > 0) {
		newText = newText + (" " + hoursPassed);
		if (hoursPassed > 1) {
			newText = newText + " hours,";
		} else {
			newText = newText + " hour,";
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	}
	if (minutesPassed > 0) {
		if (secondsPassed > 0) {
			newText = newText + (" " + minutesPassed);
		} else {
			newText = newText + (" and " + minutesPassed);
		}
		if (minutesPassed > 1) {
			newText = newText + " minutes";
		} else {
			newText = newText + " minute";
		}
		if ((secondsPassed > 0) && (hoursPassed > 0)) {
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		if ((minutesPassed > 0) || (hoursPassed > 0)) {
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		} else {
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		}
		if (secondsPassed > 1) {
			newText = newText + " seconds";
		} else {
			newText = newText + " second";
		}
	}
	newText = newText + " since you last looked at this clock.";
	timePassed.text = newText;
	clockTime = getTimer();
	this.onEnterFrame = function () {
		nowTime = new Date();
		hours = nowTime.getHours();
		if (hours > 12) {
			hours = hours - 12;
		}
		hourH._rotation = (hours / 12) * 360;
		minH._rotation = (nowTime.getMinutes() / 60) * 360;
		secH._rotation = (nowTime.getSeconds() / 60) * 360;
	};
Frame 62
	clockCode._visible = false;
Frame 64
	secondsPassed = Math.floor(getTimer() / 1000);
	if (secondsPassed >= 60) {
		minutesPassed = Math.floor(secondsPassed / 60);
		secondsPassed = secondsPassed % 60;
		if (minutesPassed >= 60) {
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			minutesPassed = minutesPassed % 60;
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	if (hoursPassed > 0) {
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		if (hoursPassed > 1) {
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		} else {
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		} else {
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		if (minutesPassed > 1) {
			newText = newText + " minutes";
		} else {
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		if ((secondsPassed > 0) && (hoursPassed > 0)) {
			newText = newText + ",";
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		if ((minutesPassed > 0) || (hoursPassed > 0)) {
			newText = newText + (" and " + secondsPassed);
		} else {
			newText = newText + (" " + secondsPassed);
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		if (secondsPassed > 1) {
			newText = newText + " seconds";
		} else {
			newText = newText + " second";
		}
	}
	newText = newText + " learning about Trigonometry. You should ask your teacher for extra credit or something.";
	timePassed.text = newText;
Symbol 20 Button
on (release) {
	play();
}
Symbol 37 Button
on (release) {
	nextFrame();
}
Symbol 50 Button
on (release) {
	gotoAndStop ("topic2");
}
Symbol 52 Button
on (release) {
	_root.onEnterFrame = null;
	nextFrame();
}
Symbol 100 Button
on (release) {
	gotoAndStop ("topic1");
}
Symbol 110 Button
on (release) {
	gotoAndStop ("topic3");
}
Symbol 114 Button
on (release) {
	gotoAndStop ("topic2");
}
Symbol 126 Button
on (release) {
	gotoAndStop ("topic4");
}
Symbol 132 Button
on (release) {
	gotoAndStop ("topic3");
}
Symbol 162 Button
on (release) {
	gotoAndStop ("topic5");
}
Symbol 173 MovieClip Frame 40
	stop();
Symbol 174 Button
on (release) {
	gotoAndStop ("topic4");
}
Symbol 190 MovieClip Frame 40
	stop();
Symbol 206 Button
on (press) {
	arrowCode._visible = true;
}
Symbol 208 Button
on (press) {
	this._visible = false;
}
Symbol 214 Button
on (release) {
	gotoAndStop ("topic6");
}
Symbol 217 Button
on (release) {
	gotoAndStop ("topic5");
}
Symbol 229 MovieClip Frame 40
	stop();
Symbol 251 Button
on (press) {
	fishCode._visible = true;
}
Symbol 258 Button
on (rollOver) {
	_parent.onEnterFrame = function () {
		fishCode._y = fishCode._y + 12;
		if (fishCode._y > fishTop) {
			fishCode._y = fishTop;
		}
	};
}
on (rollOut) {
	_parent.onEnterFrame = null;
}
Symbol 259 Button
on (rollOver) {
	_parent.onEnterFrame = function () {
		fishCode._y = fishCode._y - 12;
		if ((fishCode._y + fishCode._height) < fishBottom) {
			fishCode._y = fishBottom - fishCode._height;
		}
	};
}
on (rollOut) {
	_parent.onEnterFrame = null;
}
Symbol 260 MovieClip Frame 1
	fishTop = fishCode._y;
	fishBottom = fishTop - fishCode._height;
Symbol 264 Button
on (release) {
	gotoAndStop ("topic7");
}
Symbol 266 Button
on (release) {
	gotoAndStop ("topic6");
}
Symbol 281 Button
on (press) {
	clockCode._visible = true;
}
Symbol 291 MovieClip Frame 40
	stop();
Symbol 292 Button
on (release) {
	gotoAndStop ("topic7");
}

Library Items

Symbol 1 Graphic	Used by:Timeline
Symbol 2 Font	Used by:3 4 5 6 7 8 9 10 11 12 105 106 107 108
Symbol 3 Text	Uses:2	Used by:Timeline
Symbol 4 Text	Uses:2	Used by:Timeline
Symbol 5 Text	Uses:2	Used by:Timeline
Symbol 6 Text	Uses:2	Used by:Timeline
Symbol 7 Text	Uses:2	Used by:Timeline
Symbol 8 Text	Uses:2	Used by:Timeline
Symbol 9 Text	Uses:2	Used by:Timeline
Symbol 10 Text	Uses:2	Used by:Timeline
Symbol 11 Text	Uses:2	Used by:Timeline
Symbol 12 Text	Uses:2	Used by:Timeline
Symbol 13 Graphic	Used by:14
Symbol 14 MovieClip	Uses:13	Used by:Timeline
Symbol 15 Graphic	Used by:20
Symbol 16 Font	Used by:17 40 42 44 48 103 104 112 123 127 137 183 209 252 282 289 290
Symbol 17 Text	Uses:16	Used by:20
Symbol 18 Graphic	Used by:20
Symbol 19 Graphic	Used by:20
Symbol 20 Button	Uses:15 17 18 19	Used by:Timeline
Symbol 21 Graphic	Used by:206 208 251 258 259 281 291 Timeline
Symbol 22 Graphic	Used by:Timeline
Symbol 23 ShapeTweening	Used by:Timeline
Symbol 24 Font	Used by:25 134 157 177 186 202 210 254 274 276 278 283
Symbol 25 Text	Uses:24	Used by:Timeline
Symbol 26 Sound	Used by:Timeline
Symbol 27 Graphic	Used by:Timeline
Symbol 28 Graphic	Used by:29
Symbol 29 MovieClip	Uses:28	Used by:30
Symbol 30 MovieClip	Uses:29	Used by:Timeline
Symbol 31 Font	Used by:32 34 51 53 54 55 61 62 63 64 65 66 67 68 69 70 71 72 101 103 104 112 113 116 117 122 123 124 127 128 129 130 131 133 135 137 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 158 159 160 164 168 169 170 171 176 178 179 180 181 182 183 184 187 191 193 194 195 201 203 205 212 215 220 221 222 224 225 226 227 230 231 232 233 234 235 237 242 244 245 246 248 250 261 262 265 267 268 271 272 273 275 277 280 285 288 289 290
Symbol 32 Text	Uses:31	Used by:Timeline
Symbol 33 Graphic	Used by:37 52
Symbol 34 Text	Uses:31	Used by:37 52
Symbol 35 Graphic	Used by:37 52
Symbol 36 Graphic	Used by:37 52
Symbol 37 Button	Uses:33 34 35 36	Used by:Timeline
Symbol 38 Font	Used by:39 109 125 161 213 263 286
Symbol 39 Text	Uses:38	Used by:Timeline
Symbol 40 Text	Uses:16	Used by:Timeline
Symbol 41 Graphic	Used by:46 100 114 132 174 217 266 292
Symbol 42 Text	Uses:16	Used by:46 100 114 132 174 217 266 292
Symbol 43 Graphic	Used by:46 100 114 132 174 217 266 292
Symbol 44 Text	Uses:16	Used by:46 100 114 132 174 217 266 292
Symbol 45 Graphic	Used by:46 50 100 110 114 126 132 162 174 214 217 264 266 287 292
Symbol 46 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 47 Graphic	Used by:50 110 126 162 214 264 287
Symbol 48 Text	Uses:16	Used by:50 110 126 162 214 264 287
Symbol 49 Graphic	Used by:50 110 126 162 214 264 287
Symbol 50 Button	Uses:47 48 49 45	Used by:Timeline
Symbol 51 Text	Uses:31	Used by:Timeline
Symbol 52 Button	Uses:33 34 35 36	Used by:Timeline
Symbol 53 Text	Uses:31	Used by:Timeline
Symbol 54 Text	Uses:31	Used by:Timeline
Symbol 55 Text	Uses:31	Used by:Timeline
Symbol 56 Graphic	Used by:57
Symbol 57 MovieClip	Uses:56	Used by:189 Timeline
Symbol 58 Graphic	Used by:59
Symbol 59 MovieClip	Uses:58	Used by:Timeline
Symbol 60 Graphic	Used by:73
Symbol 61 Text	Uses:31	Used by:73
Symbol 62 Text	Uses:31	Used by:73
Symbol 63 Text	Uses:31	Used by:73
Symbol 64 Text	Uses:31	Used by:73
Symbol 65 Text	Uses:31	Used by:73
Symbol 66 Text	Uses:31	Used by:73
Symbol 67 Text	Uses:31	Used by:73
Symbol 68 Text	Uses:31	Used by:73
Symbol 69 Text	Uses:31	Used by:73
Symbol 70 Text	Uses:31	Used by:73
Symbol 71 Text	Uses:31	Used by:73
Symbol 72 Text	Uses:31	Used by:73
Symbol 73 MovieClip	Uses:60 61 62 63 64 65 66 67 68 69 70 71 72	Used by:Timeline
Symbol 74 Graphic	Used by:75
Symbol 75 MovieClip	Uses:74	Used by:Timeline
Symbol 76 Graphic	Used by:77
Symbol 77 MovieClip	Uses:76	Used by:Timeline
Symbol 78 Graphic	Used by:79
Symbol 79 MovieClip	Uses:78	Used by:Timeline
Symbol 80 Graphic	Used by:98
Symbol 81 Graphic	Used by:82
Symbol 82 MovieClip	Uses:81	Used by:98
Symbol 83 Graphic	Used by:84
Symbol 84 MovieClip	Uses:83	Used by:98
Symbol 85 Graphic	Used by:97
Symbol 86 Graphic	Used by:97
Symbol 87 Graphic	Used by:88
Symbol 88 MovieClip	Uses:87	Used by:97
Symbol 89 Graphic	Used by:97
Symbol 90 Graphic	Used by:97
Symbol 91 Graphic	Used by:97
Symbol 92 Graphic	Used by:97
Symbol 93 Graphic	Used by:97
Symbol 94 Graphic	Used by:97
Symbol 95 Graphic	Used by:97
Symbol 96 Graphic	Used by:97
Symbol 97 MovieClip	Uses:85 86 88 89 90 91 92 93 94 95 96	Used by:98
Symbol 98 MovieClip	Uses:80 82 84 97	Used by:99 216 Timeline
Symbol 99 MovieClip	Uses:98	Used by:Timeline
Symbol 100 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 101 Text	Uses:31	Used by:Timeline
Symbol 102 Graphic	Used by:Timeline
Symbol 103 Text	Uses:31 16	Used by:Timeline
Symbol 104 Text	Uses:31 16	Used by:Timeline
Symbol 105 Text	Uses:2	Used by:Timeline
Symbol 106 Text	Uses:2	Used by:Timeline
Symbol 107 Text	Uses:2	Used by:Timeline
Symbol 108 Text	Uses:2	Used by:Timeline
Symbol 109 Text	Uses:38	Used by:Timeline
Symbol 110 Button	Uses:47 48 49 45	Used by:Timeline
Symbol 111 Graphic	Used by:Timeline
Symbol 112 Text	Uses:31 16	Used by:Timeline
Symbol 113 Text	Uses:31	Used by:Timeline
Symbol 114 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 115 Graphic	Used by:Timeline
Symbol 116 Text	Uses:31	Used by:Timeline
Symbol 117 EditableText	Uses:31	Used by:118
Symbol 118 MovieClip	Uses:117	Used by:Timeline
Symbol 119 Graphic	Used by:120
Symbol 120 MovieClip	Uses:119	Used by:Timeline
Symbol 121 Graphic	Used by:Timeline
Symbol 122 Text	Uses:31	Used by:Timeline
Symbol 123 Text	Uses:31 16	Used by:Timeline
Symbol 124 Text	Uses:31	Used by:Timeline
Symbol 125 Text	Uses:38	Used by:Timeline
Symbol 126 Button	Uses:47 48 49 45	Used by:Timeline
Symbol 127 Text	Uses:31 16	Used by:Timeline
Symbol 128 Text	Uses:31	Used by:Timeline
Symbol 129 Text	Uses:31	Used by:Timeline
Symbol 130 Text	Uses:31	Used by:Timeline
Symbol 131 Text	Uses:31	Used by:Timeline
Symbol 132 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 133 Text	Uses:31	Used by:Timeline
Symbol 134 EditableText	Uses:24 136	Used by:Timeline
Symbol 135 Text	Uses:31	Used by:Timeline
Symbol 136 Font	Used by:134 137 139 157 177 182 183 185 186 202 205 210 231 234 244 248 254 261 272 274 276 277 278 283
Symbol 137 Text	Uses:31 136 16	Used by:Timeline
Symbol 138 Graphic	Used by:Timeline
Symbol 139 Text	Uses:31 136	Used by:Timeline
Symbol 140 Text	Uses:31	Used by:Timeline
Symbol 141 Text	Uses:31	Used by:Timeline
Symbol 142 Text	Uses:31	Used by:Timeline
Symbol 143 Text	Uses:31	Used by:Timeline
Symbol 144 Text	Uses:31	Used by:Timeline
Symbol 145 Text	Uses:31	Used by:Timeline
Symbol 146 Text	Uses:31	Used by:Timeline
Symbol 147 Text	Uses:31	Used by:Timeline
Symbol 148 Text	Uses:31	Used by:Timeline
Symbol 149 Text	Uses:31	Used by:Timeline
Symbol 150 Text	Uses:31	Used by:Timeline
Symbol 151 Text	Uses:31	Used by:Timeline
Symbol 152 Text	Uses:31	Used by:Timeline
Symbol 153 Text	Uses:31	Used by:Timeline
Symbol 154 Text	Uses:31	Used by:Timeline
Symbol 155 Text	Uses:31	Used by:Timeline
Symbol 156 Text	Uses:31	Used by:Timeline
Symbol 157 EditableText	Uses:24 136	Used by:Timeline
Symbol 158 Text	Uses:31	Used by:Timeline
Symbol 159 Text	Uses:31	Used by:Timeline
Symbol 160 Text	Uses:31	Used by:Timeline
Symbol 161 Text	Uses:38	Used by:Timeline
Symbol 162 Button	Uses:47 48 49 45	Used by:Timeline
Symbol 163 Graphic	Used by:Timeline
Symbol 164 Text	Uses:31	Used by:Timeline
Symbol 165 Graphic	Used by:166
Symbol 166 MovieClip	Uses:165	Used by:189 Timeline
Symbol 167 Graphic	Used by:172
Symbol 168 Text	Uses:31	Used by:172 189 Timeline
Symbol 169 Text	Uses:31	Used by:172 189 Timeline
Symbol 170 Text	Uses:31	Used by:172 189 Timeline
Symbol 171 Text	Uses:31	Used by:172 189 Timeline
Symbol 172 MovieClip	Uses:167 168 169 170 171	Used by:173
Symbol 173 MovieClip	Uses:172	Used by:Timeline
Symbol 174 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 175 Graphic	Used by:Timeline
Symbol 176 Text	Uses:31	Used by:Timeline
Symbol 177 EditableText	Uses:24 136	Used by:Timeline
Symbol 178 Text	Uses:31	Used by:Timeline
Symbol 179 Text	Uses:31	Used by:Timeline
Symbol 180 Text	Uses:31	Used by:Timeline
Symbol 181 Text	Uses:31	Used by:Timeline
Symbol 182 Text	Uses:31 136	Used by:Timeline
Symbol 183 Text	Uses:31 16 136	Used by:Timeline
Symbol 184 Text	Uses:31	Used by:Timeline
Symbol 185 Text	Uses:136	Used by:Timeline
Symbol 186 EditableText	Uses:24 136	Used by:Timeline
Symbol 187 Text	Uses:31	Used by:Timeline
Symbol 188 Graphic	Used by:189
Symbol 189 MovieClip	Uses:188 57 166 168 169 170 171	Used by:190
Symbol 190 MovieClip	Uses:189	Used by:Timeline
Symbol 191 Text	Uses:31	Used by:Timeline
Symbol 192 Graphic	Used by:Timeline
Symbol 193 Text	Uses:31	Used by:Timeline
Symbol 194 Text	Uses:31	Used by:Timeline
Symbol 195 Text	Uses:31	Used by:Timeline
Symbol 196 Font	Used by:197 198 199 200 238 239 240 241
Symbol 197 Text	Uses:196	Used by:Timeline
Symbol 198 Text	Uses:196	Used by:Timeline
Symbol 199 Text	Uses:196	Used by:Timeline
Symbol 200 Text	Uses:196	Used by:Timeline
Symbol 201 Text	Uses:31	Used by:Timeline
Symbol 202 EditableText	Uses:24 136	Used by:Timeline
Symbol 203 Text	Uses:31	Used by:Timeline
Symbol 204 Graphic	Used by:Timeline
Symbol 205 Text	Uses:31 136	Used by:Timeline
Symbol 206 Button	Uses:21	Used by:Timeline
Symbol 207 Graphic	Used by:211 260 284
Symbol 208 Button	Uses:21	Used by:211 260 284
Symbol 209 Text	Uses:16	Used by:211
Symbol 210 EditableText	Uses:24 136	Used by:211
Symbol 211 MovieClip	Uses:207 208 209 210	Used by:Timeline
Symbol 212 Text	Uses:31	Used by:Timeline
Symbol 213 Text	Uses:38	Used by:Timeline
Symbol 214 Button	Uses:47 48 49 45	Used by:Timeline
Symbol 215 Text	Uses:31	Used by:Timeline
Symbol 216 MovieClip	Uses:98	Used by:Timeline
Symbol 217 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 218 Graphic	Used by:219
Symbol 219 MovieClip	Uses:218	Used by:Timeline
Symbol 220 Text	Uses:31	Used by:Timeline
Symbol 221 Text	Uses:31	Used by:Timeline
Symbol 222 Text	Uses:31	Used by:Timeline
Symbol 223 Graphic	Used by:228 Timeline
Symbol 224 Text	Uses:31	Used by:228 Timeline
Symbol 225 Text	Uses:31	Used by:228 Timeline
Symbol 226 Text	Uses:31	Used by:228 Timeline
Symbol 227 Text	Uses:31	Used by:228 Timeline
Symbol 228 MovieClip	Uses:223 224 225 226 227	Used by:229
Symbol 229 MovieClip	Uses:228	Used by:Timeline
Symbol 230 Text	Uses:31	Used by:Timeline
Symbol 231 Text	Uses:31 136	Used by:Timeline
Symbol 232 Text	Uses:31	Used by:Timeline
Symbol 233 Text	Uses:31	Used by:Timeline
Symbol 234 Text	Uses:31 136	Used by:Timeline
Symbol 235 Text	Uses:31	Used by:Timeline
Symbol 236 Graphic	Used by:Timeline
Symbol 237 Text	Uses:31	Used by:Timeline
Symbol 238 Text	Uses:196	Used by:Timeline
Symbol 239 Text	Uses:196	Used by:Timeline
Symbol 240 Text	Uses:196	Used by:Timeline
Symbol 241 Text	Uses:196	Used by:Timeline
Symbol 242 Text	Uses:31	Used by:Timeline
Symbol 243 Font	Used by:244 289 290
Symbol 244 Text	Uses:31 136 243	Used by:Timeline
Symbol 245 Text	Uses:31	Used by:Timeline
Symbol 246 Text	Uses:31	Used by:Timeline
Symbol 247 Graphic	Used by:Timeline
Symbol 248 Text	Uses:31 136	Used by:Timeline
Symbol 249 Graphic	Used by:Timeline
Symbol 250 Text	Uses:31	Used by:Timeline
Symbol 251 Button	Uses:21	Used by:Timeline
Symbol 252 Text	Uses:16	Used by:260
Symbol 253 Graphic	Used by:260
Symbol 254 EditableText	Uses:24 136	Used by:255
Symbol 255 MovieClip	Uses:254	Used by:260
Symbol 256 Graphic	Used by:257
Symbol 257 MovieClip	Uses:256	Used by:260
Symbol 258 Button	Uses:21	Used by:260
Symbol 259 Button	Uses:21	Used by:260
Symbol 260 MovieClip	Uses:207 208 252 253 255 257 258 259	Used by:Timeline
Symbol 261 Text	Uses:31 136	Used by:Timeline
Symbol 262 EditableText	Uses:31	Used by:Timeline
Symbol 263 Text	Uses:38	Used by:Timeline
Symbol 264 Button	Uses:47 48 49 45	Used by:Timeline
Symbol 265 Text	Uses:31	Used by:Timeline
Symbol 266 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 267 Text	Uses:31	Used by:Timeline
Symbol 268 Text	Uses:31	Used by:Timeline
Symbol 269 Graphic	Used by:270
Symbol 270 MovieClip	Uses:269	Used by:Timeline
Symbol 271 Text	Uses:31	Used by:Timeline
Symbol 272 Text	Uses:31 136	Used by:Timeline
Symbol 273 Text	Uses:31	Used by:Timeline
Symbol 274 EditableText	Uses:24 136	Used by:Timeline
Symbol 275 Text	Uses:31	Used by:Timeline
Symbol 276 EditableText	Uses:24 136	Used by:Timeline
Symbol 277 Text	Uses:31 136	Used by:Timeline
Symbol 278 EditableText	Uses:24 136	Used by:Timeline
Symbol 279 Graphic	Used by:Timeline
Symbol 280 Text	Uses:31	Used by:Timeline
Symbol 281 Button	Uses:21	Used by:Timeline
Symbol 282 Text	Uses:16	Used by:284
Symbol 283 EditableText	Uses:24 136	Used by:284
Symbol 284 MovieClip	Uses:207 208 282 283	Used by:Timeline
Symbol 285 Text	Uses:31	Used by:Timeline
Symbol 286 Text	Uses:38	Used by:Timeline
Symbol 287 Button	Uses:47 48 49 45	Used by:Timeline
Symbol 288 EditableText	Uses:31	Used by:Timeline
Symbol 289 EditableText	Uses:16 31 243	Used by:Timeline
Symbol 290 EditableText	Uses:16 31 243	Used by:291
Symbol 291 MovieClip	Uses:21 290	Used by:Timeline
Symbol 292 Button	Uses:41 42 43 44 45	Used by:Timeline
Symbol 293 Sound	Used by:Timeline

Instance Names

"ticker"	Frame 1	Symbol 14 MovieClip
"mc_arrow"	Frame 22	Symbol 57 MovieClip
"tank"	Frame 22	Symbol 59 MovieClip
"hourH"	Frame 22	Symbol 75 MovieClip
"secH"	Frame 22	Symbol 77 MovieClip
"minH"	Frame 22	Symbol 79 MovieClip
"fish"	Frame 22	Symbol 99 MovieClip
"degClip"	Frame 26	Symbol 118 MovieClip
"redLine"	Frame 26	Symbol 120 MovieClip
"mc_arrow"	Frame 34	Symbol 57 MovieClip
"mc_arrow"	Frame 41	Symbol 57 MovieClip
"arrowCode"	Frame 43	Symbol 211 MovieClip
"tank"	Frame 44	Symbol 59 MovieClip
"fish"	Frame 44	Symbol 99 MovieClip
"fishCode"	Frame 53	Symbol 260 MovieClip
"hourH"	Frame 54	Symbol 75 MovieClip
"secH"	Frame 54	Symbol 77 MovieClip
"minH"	Frame 54	Symbol 79 MovieClip
"timePassed"	Frame 54	Symbol 262 EditableText
"clockCode"	Frame 62	Symbol 284 MovieClip
"timePassed"	Frame 64	Symbol 288 EditableText
"numDegrees"	Symbol 118 MovieClip Frame 1	Symbol 117 EditableText
"mc_arrow"	Symbol 189 MovieClip Frame 1	Symbol 57 MovieClip
"fishCode"	Symbol 260 MovieClip Frame 1	Symbol 255 MovieClip

Labels

"topic1"	Frame 21
"topic2"	Frame 24
"topic3"	Frame 27
"topic4"	Frame 34
"topic5"	Frame 44
"topic6"	Frame 54
"topic7"	Frame 63