What is the general solution for 5sin(pi/3 x)=2 ?

The general solution for 5sin(pi/3 x)=2 is x=(3*0.41151…)/pi+6n,x=3-(3*0.41151…)/pi+6n

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5sin(pi/3 x)=2

5 sin (\frac{π}{3} x) = 2

x = \frac{3 \cdot 0.41151 \dots}{π} + 6 n, x = 3 - \frac{3 \cdot 0.41151 \dots}{π} + 6 n

Solution steps

5 sin (\frac{π}{3} x) = 2

Divide both sides by

5

sin (\frac{π}{3} x) = \frac{2}{5}

Apply trig inverse properties

\frac{π}{3} x = arcsin (\frac{2}{5}) + 2 πn, \frac{π}{3} x = π - arcsin (\frac{2}{5}) + 2 πn

Solve

\frac{π}{3} x = arcsin (\frac{2}{5}) + 2 πn : x = \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

Solve

\frac{π}{3} x = π - arcsin (\frac{2}{5}) + 2 πn : x = 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

x = \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n, x = 3 - \frac{3 arcsin ( \frac{2}{5} )}{π} + 6 n

Show solutions in decimal form

x = \frac{3 \cdot 0.41151 \dots}{π} + 6 n, x = 3 - \frac{3 \cdot 0.41151 \dots}{π} + 6 n

4 cos^{2} (x) - 5 cos (x) + 1 = 0

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csc^{2} (x) = 2 cot^{2} (x)

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

5 sin (x) cos (x) + 4 cos (x) = 0

What is the general solution for 5sin(pi/3 x)=2 ?
The general solution for 5sin(pi/3 x)=2 is x=(3*0.41151…)/pi+6n,x=3-(3*0.41151…)/pi+6n