# Find two solutions for Cosine theta = 1/2 for

Find two solutions for Cosine theta = 1/2 for....

1. Find two solutions for Cosine theta = 1/2 for 0 degrees less than or equal to theta less than or equal to 360 degrees. Express answers in degrees and radians.

## Homework Equations

3. I know that Cosine theta = 1/2 gives you 60 degrees which is also pie/3 radians. I dont know what the other solution is though. Can anyone help?

## Answers and Replies

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eumyang
Homework Helper

Are you familiar with reference angles? See http://www.analyzemath.com/Angle/reference_angle.html" [Broken].

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Im familiar with reference angles. I just didnt know to use them but since you mentioned it, what comes to mind is taking 60 degrees from 360 degrees. That leaves me with 300 degrees. From there, i dont know how to proceed.

Well whats cos 300?

yea after a while i figured it out. cos 300= 1/2

eumyang
Homework Helper

No, it's not. cos 300 = -0.02209661927868394268907560278956...

Or perhaps you meant cos 300° = 1/2. The degree sign is important. Without it, I have to assume you mean radians. Speaking of which, don't forget that you were asked to find answers in degrees and radians.

maybe i can help
since cos 60 = 1/2 , i'll use x as theta
=> cos x = cos 60

1. cos x = 60 + k.360
=> x = 60

2. cos theta = -60 + k.360
=> x = 300

in degree x = {60, 300}
in radian x = {1/3 pi rad, 5/3 pi rad}