Solve for theta in the interval 0 to 180

Question

cos theta= radical cos theta

Answer 1

cosθ = √(cosθ)

 

square both sides:  cos²θ = cosθ

 

cos²θ - cosθ = 0

 

cosθ(cosθ - 1) = 0

 

cosθ = 0 or cosθ = 1

 

if cosθ = 0 and 0° ≤ θ ≤ 180°, then θ = 90°

 

if cosθ = 1 and 0° ≤ θ ≤ 180°, then θ = 0°

 

Solutions:  0°, 90°