List four values of 𝜃, between -360° and 360°, to satisfy the statements. Round angles to the nearest degree.

Question

1. cos0-cos52
2. cos0=-cos37
3. cos0=0.75
4. cos0= -0.37

Answer 1

In general, if 0° < θ < 180° then

cos(θ) = cos(-θ) = cos(360° - θ) = cos(-360° + θ)

This identity then gives us four solutions for each of the four questions:

1. θ = 52°, -52°, 308°, -308°

2. -cos(37°) = cos(180° - 37°) = cos(143°)

θ = 143°, -143°, 217°, -217°

3. θ = 41°, -41°, 319°, -319°

4. cos(68°) = 0.37, therefore cos(112°) = -0.37

θ = 112°, -112°, 248°, -248°