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

The general solution for 3sin(pi/3 x)=2 is x=(3*0.72972…)/pi+6n,x=3-(3*0.72972…)/pi+6n

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3sin(pi/3 x)=2

3 sin (\frac{π}{3} x) = 2

x = \frac{3 \cdot 0.72972 \dots}{π} + 6 n, x = 3 - \frac{3 \cdot 0.72972 \dots}{π} + 6 n

Solution steps

3 sin (\frac{π}{3} x) = 2

Divide both sides by

3

sin (\frac{π}{3} x) = \frac{2}{3}

Apply trig inverse properties

\frac{π}{3} x = arcsin (\frac{2}{3}) + 2 πn, \frac{π}{3} x = π - arcsin (\frac{2}{3}) + 2 πn

Solve

\frac{π}{3} x = arcsin (\frac{2}{3}) + 2 πn : x = \frac{3 arcsin ( \frac{2}{3} )}{π} + 6 n

Solve

\frac{π}{3} x = π - arcsin (\frac{2}{3}) + 2 πn : x = 3 - \frac{3 arcsin ( \frac{2}{3} )}{π} + 6 n

x = \frac{3 arcsin ( \frac{2}{3} )}{π} + 6 n, x = 3 - \frac{3 arcsin ( \frac{2}{3} )}{π} + 6 n

Show solutions in decimal form

x = \frac{3 \cdot 0.72972 \dots}{π} + 6 n, x = 3 - \frac{3 \cdot 0.72972 \dots}{π} + 6 n

cos^{2} (x) = \frac{1}{3}

4 cos (θ) = 1 + 2 cos (θ)

tan (θ) = \frac{3}{3}

2 sin (3 x) + 2 = 4

sin (4 x) - 2 sin (2 x) = 0

What is the general solution for 3sin(pi/3 x)=2 ?
The general solution for 3sin(pi/3 x)=2 is x=(3*0.72972…)/pi+6n,x=3-(3*0.72972…)/pi+6n