Suppose cos Θ = w and 0 < Θ < π/2. Find each of the following: cos (-Θ) cos (180o + Θ) cos (180o - Θ)

Answer 1

cosx=cos(-x)

if cosx =w, then cos(-x) also = w

that's a property of an even function

cosine is an even function

as it's symmetric about the y-axis

just look at its graph, if you put a mirror on the y-axis, the graph on the left is a mirror image of the graph on the right.

cos(180+x) = negative w = -w

adding 180 to the angle just puts it in the 3rd quadrant, changing the sign of the cosine

going from x to 180-x just changes the sign of the cosine, from w to -w

cos(180-x) also changes the angle, but this time from 1st to 2nd quadrant, which also changes the sign to negative w

cos(180-x)= -w

If x=60 cos60=1/2

then cos(180-x)=cos(180-60)=cos120 = -1/2