Rules for finding cos values?

Question

To find cos(150deg), I tried to use the formula for adding cos 90+60, but this gives a different answer than cos 180-30. How do you know when to add or subtract when there seem to be different ways of getting the answer?

Answer 1

You have to use the unit circle. The angle of 150 is the same as 180-150 or 30, but you have to remember that cos is negative in the 2nd quad.  

Answer 2

either way you should get the same answer.

cos (90+60)=cos90cos60-sin90sin60

=0(1/2)-1(√3/2)

=√3/2

cos (180-30)=cos180cos30+sin180sin30

=-1(√3/2)+0(1/2)

=√3/2

Answer 3

You made some mistake. cos(90°+60°) is exactly the same as cos(180°-30°) if you apply the formulas correctly. You shouldn't be getting different answers. Anyways, I'd go with cos(90°+60°) because I assume you know how to figure out sine/cosine for 90° and 60° right? So that's the easier choice.

cos(90°+60°) =cos(90°)cos(60°)-sin(90°)sin(60°)

=0(1/2)-1(√3/2)

=0-√3/2

=-√(3)/2