Question

Find an exact value.

cos 165°

quantity square root of six minus square root of two divided by four.
quantity square root of two minus square root of six divided by four.
quantity square root of two plus square root of six divided by four.
quantity negative square root of six minus square root of two divided by four.

Answer 1

\[\cos 165^{\circ} = -\cos (180^{\circ} - 165^{\circ})=-\cos(15^{\circ})\]\[= - \cos(45^{\circ} - 30^{\circ})\]

Answer 2

I thought you would do cos(165)=cos(120+45) for that part?

Answer 3

Anything that works...

Answer 4

Okay can you help me do the problem that way?

Answer 5

\[\cos(120 + 45) = \cos 120 \cos 45 - \sin 120 \sin 45\]Do you know the values of the four trig-ratios?

Answer 6

Would I use the unit circle for that?

Answer 7

yes, you can use the unit circle (at least to figure out the correct sign)

for example, cos 120

on the unit circle we have