Solve for the exact solutions in the interval [ 0 , 2 π ) . List your answers separated by a comma, if it has no real solutions, enter DNE.

Answer 1

cos(2θ)=sin(θ) or we can say cos(2θ)=cos(π/2-θ)

2θ=2kπ ± (π/2-θ)

with positive sign:

2θ=2kπ + (π/2-θ), thus θ=(2/3)kπ+π/6

k=0→ θ=π/6, k=1→ θ=5π/6, k=3→ θ=3π/2

With negative sign:

2θ=2kπ - (π/2-θ), thus θ=2kπ - π/2

k=1→ θ=3π/2

Thus answers are π/6, 5π/6, 3π/2