# Homework Help: Find two solutions for Cosine theta = 1/2 for

1. Jul 4, 2011

### infiniteking1

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.

2. Relevant 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?

2. Jul 4, 2011

### eumyang

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

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

Last edited by a moderator: May 5, 2017
3. Jul 4, 2011

### infiniteking1

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

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.

4. Jul 5, 2011

### Ivan92

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

Well whats cos 300?

5. Jul 5, 2011

### infiniteking1

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

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

6. Jul 5, 2011

### eumyang

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

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.

7. Jul 6, 2011

### kevinfrankly

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

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}