What is the general solution for sin(2x)=(sqrt(3))/2 ,0<= x<= 2pi ?

The general solution for sin(2x)=(sqrt(3))/2 ,0<= x<= 2pi is x= pi/6 ,x= pi/3 ,x=(7pi)/6 ,x=(4pi)/3

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sin(2x)=(sqrt(3))/2 ,0<= x<= 2pi

sin (2 x) = \frac{3}{2}, 0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{7 π}{6}, x = \frac{4 π}{3}

Solution steps

sin (2 x) = \frac{3}{2}, 0 \leq x \leq 2 π

General solutions for

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

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

Solve

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

Solve

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

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

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{7 π}{6}, x = \frac{4 π}{3}

2 tan (x) = 1 - tan^{2} (x)

3 sin (θ) + 3 = 2 cos^{2} (θ)

cos (x) = - \frac{5}{6}

2 sin (\frac{x}{2}) - 3 = 0

2 sin^{2} (θ) = sin (θ) + 1

What is the general solution for sin(2x)=(sqrt(3))/2 ,0<= x<= 2pi ?
The general solution for sin(2x)=(sqrt(3))/2 ,0<= x<= 2pi is x= pi/6 ,x= pi/3 ,x=(7pi)/6 ,x=(4pi)/3