What is the general solution for 6sin(2x)=3 ?

The general solution for 6sin(2x)=3 is x= pi/(12)+pin,x=(5pi)/(12)+pin

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6sin(2x)=3

6 sin (2 x) = 3

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Solution steps

6 sin (2 x) = 3

Divide both sides by

6

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

General solutions for

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

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

Solve

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

Solve

2 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

- cos (x) = - sin^{2} (x) - 1, 0 \leq x \leq 2 π

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

tan (t) = 4

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

1 + 4 \cdot sin (x) = 2

What is the general solution for 6sin(2x)=3 ?
The general solution for 6sin(2x)=3 is x= pi/(12)+pin,x=(5pi)/(12)+pin