Question

Solve the following equations giving any roots in terms of pi in the .......?
interval -2pi ≤ 0 ≤ 2pi.

a) 2cos²Θ + sin²Θ = 0

b) 2cos²Θ + sin²Θ = 1

c) 2cos²Θ + sin²Θ = 2

Answer 1

First convert cos^2 theta to 1 - sin^2 theta. Then treat sin^2 as a new variable x and solve for that using quadratic equation procedures.

Answer 2

I will do the last one for you

2cos²Θ + sin²Θ = 2
2cos²Θ + 1 - cos²Θ = 2
cos²Θ = 1
cosΘ = ±1


in degrees, Θ = 0º or 180º or 360º
in radians: Θ = 0 pi or 2pi