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

The general solution for 3sin(pi/5 x)=2 is x=(5*0.72972…)/pi+10n,x=5-(5*0.72972…)/pi+10n

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3sin(pi/5 x)=2

3 sin (\frac{π}{5} x) = 2

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

Solution steps

3 sin (\frac{π}{5} x) = 2

Divide both sides by

3

sin (\frac{π}{5} x) = \frac{2}{3}

Apply trig inverse properties

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

Solve

\frac{π}{5} x = arcsin (\frac{2}{3}) + 2 πn : x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

Solve

\frac{π}{5} x = π - arcsin (\frac{2}{3}) + 2 πn : x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

x = \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n, x = 5 - \frac{5 arcsin ( \frac{2}{3} )}{π} + 10 n

Show solutions in decimal form

x = \frac{5 \cdot 0.72972 \dots}{π} + 10 n, x = 5 - \frac{5 \cdot 0.72972 \dots}{π} + 10 n

11 = 3 csc^{2} (x) + 7

cos (x) tan (x) = \frac{1}{2}

4 sin^{2} (x) = 1 - 4 cos (x)

- 100 sin (10 x) = 0

2 sin (x) = csc (x) - 6, 0 \leq x < 2 π

What is the general solution for 3sin(pi/5 x)=2 ?
The general solution for 3sin(pi/5 x)=2 is x=(5*0.72972…)/pi+10n,x=5-(5*0.72972…)/pi+10n