Problem:

Question

cos[arccos(-sqrt3/2)-arcsin(-1/2)]

This is what I have:
cos [(5pi/6)-(11pi/6)]
cos (-6pi/6) or -pi
giving an answer of -1

What I am wondering is should I use the (11pi/6) or should I use (-pi/6) because of the restrictions on arcsin x (-pi/2)<=x<=(pi/2)

Thank you in advance.

Answer 1

I would use the smaller angle. It should not matter on the final answer.

Answer 2

Thank you very much.

The answer doesn't change, but my trig teacher wants to see all of work, and I just wasn't sure which figure to use.