What is the general solution for 2sin(2θ)=-sqrt(3) ?

The general solution for 2sin(2θ)=-sqrt(3) is θ=(2pi)/3+pin,θ=(5pi)/6+pin

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2sin(2θ)=-sqrt(3)

2 sin (2 θ) = - 3

θ = \frac{2 π}{3} + πn, θ = \frac{5 π}{6} + πn

Solution steps

2 sin (2 θ) = - 3

Divide both sides by

2

sin (2 θ) = - \frac{3}{2}

General solutions for

sin (2 θ) = - \frac{3}{2}

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

Solve

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

Solve

2 θ = \frac{5 π}{3} + 2 πn : θ = \frac{5 π}{6} + πn

θ = \frac{2 π}{3} + πn, θ = \frac{5 π}{6} + πn

- 4 cot^{2} (x) = 1 + 2 cot (x) - 3 cot^{2} (x)

tan (x + \frac{π}{4}) - tan (x - \frac{π}{4}) = 3

cos (x) (2 sin (x) - 2) = 0

2 sin^{2} (θ) - 3 sin (θ) = - 1

4 cos^{2} (θ) + 2 = 3

What is the general solution for 2sin(2θ)=-sqrt(3) ?
The general solution for 2sin(2θ)=-sqrt(3) is θ=(2pi)/3+pin,θ=(5pi)/6+pin