for the following problems let theta = 200 degrees,

Question

for the following problems let theta = 200 degrees, and if cos theta = cos 200 = k, then find all the value of theta in the interval 0 <= theta <= 360 such that:

1. cos theta = k

Answer 1

Recall that as 0 ≤ θ < 360º, cosθ monotonically decreases from 1 to –1 (at θ = 180º) then monotonically increases again to 1. So cosθ takes every value in [–1,1] exactly twice. By symmetry, cosθ = cos(360º–θ) and in particular k = cos200º = cos160º.