[MOVED] getting equation from a periodic function

[kidwizz]

I have a test coming up soon, and the following exercises are on the revision sheet. But I don't remember this from class.

I'm supposed to look at these graphs and figure out the equations that generated them. (The graphs are in radians, by the way.) How would I go about doing that?

Thank you!
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Edited by stapel

 

[tkhunny]

First, this is a slightly unfair question. sin(x) = cos(pi - x) When it says "the" equation, I get nervous. If the answer key says some vesion of the sine and you invent a correct response that is some version of the cosine, will it get marked "wrong"?

A good rule of thumb: If it goes through the Origin, figure it as a sine function. Look at the amplitude and period and you are done.

If a maximum value is at x = 0, the Y-axis, figure it as a cosine function. Look at the amplitude and period and you are done.

ANYTHING else, you probably want to think of a sine function, but now you have three things to worry about, amplitude and period, as before, but phase shift as well.

Your first one:
Function: sine
Amplitude: 1
Period: pi/2

Second one:
Function: cosine
Amplitude: 1
Period: 4*pi

Third one:
Function: sine
Amplitude: 1
Period: pi
Phase Shift: -pi/12 <== Watch the sign.

There are many solutinos, even with the information I catalogued. Just build one that is correct. If someone marks it wrong, feel free to go show them why youare right.