Question

Hi:) anyone able to explain why at the TOP , they said cOS (180-0) = -cos 0

but for example 2 ,
cOS 0 = - cOS (180 - 0) ?

Answer 1

cos (180° -θ)= -cosθ

-cos θ= cos (180° -θ)

(-cos θ)(-1)= -cos (180° -θ) (multiply by -1 on both sides)

cosθ= -cos (180° -θ) (simplify)

Note that the question is cos 154° not -cos 154°.

See attached picture:

Draw a line at 154° (dont need to be exactly 154°- just between 90° and 180°) and label the reference angle. The reference angle lies in the 2nd quadrant. In the 2nd quadrant, only the sine of an angle is positive. All the others are negative (cosine, tangent).

Reference angle= 180° -154°= 26°

Thus cos 154°= -cos 26°