Supposedly there are four possible solutions. My professor provided a worksheet that says cos(2pi/3) and cos(4pi/3) both equal -1/2, and cos(pi/3) and cos(5pi/3) both equal 1/2. How would I go about finding the other two values that equal -1/2??

The trig functions have periods. That is, they repeat after so long.

Cosine has period of

That is, they it repeats every 2Pi.

i.e. and so on

Use this to find the values where it equals cos(x)=-1/2.



Now, enter integer values in for C. 0,1,2,3,.

Try C=0 and we get

Which

If C=1, we get



And so on and so on.

Note the difference between

If you want the interval , simply use the formula I gave you and root them out.

Does that help a little more?

I bet it does. All you have to do is plug in integer values of C to find what radian measure gives -1/2 for your cosine

Thank you. This is kind of helpful, but I am still pretty confused as to why there can only be 4 possible values... aren't there endless values?

That's because you only want those in a certain interval. Most likely from 0 to 2Pi

The two in that interval are

For 1/2. they are

I am assuming 0 to 2Pi is the interval you are using. You must know that.

Look at the graph of cos(x). That will help visualize it.

I really appreciate all of your help galactus. I will find out what is going on with the wording of the question and let you know.

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