What is the general solution for cos(2θ)=-1/2 ,0<= θ<2pi ?

The general solution for cos(2θ)=-1/2 ,0<= θ<2pi is θ= pi/3 ,θ=(2pi)/3 ,θ=(4pi)/3 ,θ=(5pi)/3

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cos(2θ)=-1/2 ,0<= θ<2pi

cos (2 θ) = - \frac{1}{2}, 0 \leq θ < 2 π

θ = \frac{π}{3}, θ = \frac{2 π}{3}, θ = \frac{4 π}{3}, θ = \frac{5 π}{3}

Solution steps

cos (2 θ) = - \frac{1}{2}, 0 \leq θ < 2 π

General solutions for

cos (2 θ) = - \frac{1}{2}

2 θ = \frac{2 π}{3} + 2 πn, 2 θ = \frac{4 π}{3} + 2 πn

Solve

2 θ = \frac{2 π}{3} + 2 πn : θ = \frac{π}{3} + πn

Solve

2 θ = \frac{4 π}{3} + 2 πn : θ = \frac{2 π}{3} + πn

θ = \frac{π}{3} + πn, θ = \frac{2 π}{3} + πn

Solutions for the range

0 \leq θ < 2 π

θ = \frac{π}{3}, θ = \frac{2 π}{3}, θ = \frac{4 π}{3}, θ = \frac{5 π}{3}

tan (x) tan (2 x) = 1

2 sin^{2} (x) + 7 sin (x) = 4

22 cos (θ) + 4 = 6

sin (x) + cos (x) = \frac{1}{2}

6 sin^{2} (x) + 9 sin (x) + 3 = 0

What is the general solution for cos(2θ)=-1/2 ,0<= θ<2pi ?
The general solution for cos(2θ)=-1/2 ,0<= θ<2pi is θ= pi/3 ,θ=(2pi)/3 ,θ=(4pi)/3 ,θ=(5pi)/3