# Thread: Is this trigonometric identity question correct?

1. ## Is this trigonometric identity question correct?

Given cosθ=-3/5 and π < θ < 3π/2, use an appropriate trigonometric identity to evaluate exactly.

1) cos θ/2

I got :

√(1+cosθ/2) = √(1+(-3/5)/2) = √((2/5)/2) = √(5)/5

I realize that they are referring to quadrant 3, I'm not really sure why that is relevant in the question. Could someone please explain that to me? And also if I have the right answer?

Thank you very much!

2. ## Re: Is this trigonometric identity question correct?

Hey curt26.

Just to confirm, are you using the double angle relationship (cos(2x) in terms of cos(x)) to answer your question?

3. ## Re: Is this trigonometric identity question correct?

Sorry for the late reply. I have limited internet access when I'm out of town working.

No I was using the Half-angle identity...Is that not correct?

Thank you

4. ## Re: Is this trigonometric identity question correct?

Originally Posted by curt26
Sorry for the late reply. I have limited internet access when I'm out of town working.
No I was using the Half-angle identity...Is that not correct?
From the given you know that $\frac{\pi }{2} < \frac{\theta }{2} < \frac{{3\pi }}{4}$ so $\cos \left( {\frac{\theta }{2}} \right) = - \sqrt {\frac{{1 + \cos (\theta )}}{2}}$

5. ## Re: Is this trigonometric identity question correct?

Yes thank you. That's the formula I used