What is the general solution for 2sin(x/3)=1 ?

The general solution for 2sin(x/3)=1 is x= pi/2+6pin,x=(5pi)/2+6pin

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2sin(x/3)=1

2 sin (\frac{x}{3}) = 1

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

Solution steps

2 sin (\frac{x}{3}) = 1

Divide both sides by

2

sin (\frac{x}{3}) = \frac{1}{2}

General solutions for

sin (\frac{x}{3}) = \frac{1}{2}

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

Solve

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

Solve

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

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

sin^{2} (x) - 3 cos (x) = 3

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

6 sin (2 x) = 4

cos^{2} (x) + sin (x) = - 1

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

What is the general solution for 2sin(x/3)=1 ?
The general solution for 2sin(x/3)=1 is x= pi/2+6pin,x=(5pi)/2+6pin