Question

Solve the equation for   π).

A.) 2

 

Answer 1

2 cos^2θ-cosθ=1

2 cos^2θ-cosθ-1=0

2 cos^2θ-2cosθ+cosθ-1=0

2cosθ(cosθ-1)+1(cosθ-1)=0

cosθ-1-=0 and 2cosθ+1=0

cosθ-1-=0

cosθ=1

cosθ=cos(0)

θ=2nπ

n=0

θ=0

2cosθ+1=0

2cosθ=-1

cosθ=-1/2

cosθ=cos(2π/3)

θ=2nπ±2π/3

n=0

θ=2π/3

n=1

θ=2π-2π/3=4π/3

Final solutions are θ=0,2π/3,4π/3