# Sine and Circles :(

This topic is 5405 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

I was in my Pre-Cal class today, and we were talking about a ferris wheel. We were supposed to make a function using sine to represent a person's distance off the ground as time passes and they go around the ferris wheel. I learned what the teacher wanted me to learn, but I was curious about why we used sine (whose wave is more like a squashed pointy semicircle) instead of a bunch of semicircles (which would fit the ferris wheel's O shape, and I thought should represent the person's distance off the ground better) in a row to make up the wave. I know that the sine curve is right because a bunch of people smarter than me say it is, but I don't know WHY it's right. :( I asked the teacher, and she got mad and yelled. :(

##### Share on other sites
So really your question is this:

Why don't sine and cosine look like semi-circles linked together?

The answer is simple. The inputs to the sine and cosine functions are the angle. The X axis in a graph of sine and cosine doesn't represent the same X as a graph of a circle.

##### Share on other sites
I know that sine deals with angles, which is why I was wondering why we used sine when determining how high the person is off the ground. I don't see where an angle is put into the problem. X was supposed to be how much time had passed, not an angle! :(

##### Share on other sites
I had the same question when I took PreCal this summer. If you notice that you can follow surface area, it can goe from 1,0, 0,1 -1,0 to 0,-1 an infinity amount of times. Like if you have 380 degrees, it's really just 20 degrees. You can go around the circle and increase or decrese your degrees as much as you want, that's why the wave repeats forever. Is that your question?

##### Share on other sites
Look at the Height of 1 certain chair on the Ferris Wheel. What does it do...

It goes up and down up and down... at exactly the same rate as a sin wave does.

##### Share on other sites
Hint: You can plot a circle with a radius of 1 with [cosine(angle), sine(angle)], for 0° - 360°.

##### Share on other sites
Also, you'd need to know the time to know what the angle is. I assume they tell you how fast the wheel is turning. . .

##### Share on other sites
Thanks for all the replies!

My brother explained how the x doesn't change constantly with time in the semicircles. When you're moving mainly vertically on a ferris wheel, you're going slower horizontally, which the sine graph shows. (He explained it, which I understand now, but couldn't explain myself...)

##### Share on other sites
You might've figured this out, but I'll chime in anyways.

Quote:
 Original post by SirGorthonI know that sine deals with angles, which is why I was wondering why we used sine when determining how high the person is off the ground. I don't see where an angle is put into the problem. X was supposed to be how much time had passed, not an angle! :(

What is it that has the same speed over time? Horiz. pos? No - it goes back and forth. Vert. pos? No - up/down. Angle? Yes. The angle the wheel is at changes in time at the same rate, the same RPM. There is a direct relationship between the angle the wheel is at and the amount of time that's past. Eg, if the wheel were spinning at 2 RPM, and 3 minutes had passed, it would be at an angle of 2 * 3 * 360 (a single revolution). That is, 2160 degrees from where it started. This is the angle that's used in the problem.

##### Share on other sites
~hi~

Try plotting this yourself...

Use graf paper and draw x,y axis lines with origin at the center of paper.

Make a table of these three values...(from basic right triangle formulas)

A, x=cos(A), y=sin(A)

Start with A=0 degrees and plug A into the other two functions.

For A, use 0,30,60,90,...etc...until you reach 360 degrees.

Use calculator to get the x and y values from the cos and sin, but plot x,y points by hand. For students I tutor that are confused about how "sine" makes a circle, doing this one graf seems to help them see what is going on...if they plot the x,y values by hand, I guess its the personal creation thing that clicks with people I dunno.

table should look like this...but plug the numbers in for cos and sin

Angle, x value , y value
-------------------------
0, cos(0), sin(0)
30, cos(30), sin(30)
60, cos(60), sin(60)
90, cos(90), sin(90)
120, cos(120), sin(120)
:
:
360, x=cos(360), y=sin(360)

you find that at A=360, both the resultant x,y values are back back at the original x,y values when A=0. Starting all over, going in circles, round and round, sounds like me doing homework.

• 21
• 16
• 9
• 17
• 13
×

## Important Information

GameDev.net is your game development community. Create an account for your GameDev Portfolio and participate in the largest developer community in the games industry.

Sign me up!