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

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

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2sin(2x)=-sqrt(3)

2 sin (2 x) = - 3

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

Solution steps

2 sin (2 x) = - 3

Divide both sides by

2

sin (2 x) = - \frac{3}{2}

General solutions for

sin (2 x) = - \frac{3}{2}

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

Solve

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

Solve

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

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

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

tan (x) = \frac{5}{2}

4 sin (x) cos (x) = 3

3 sin (x) + 4 cos (x) = 2

cot^{2} (x) - 6 cot (x) + 5 = 0, 0 \leq x \leq 2 π

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