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

The general solution for 3sin(pi/2 x)=2 is x=(2*0.72972…)/pi+4n,x=2-(2*0.72972…)/pi+4n

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3sin(pi/2 x)=2

3 sin (\frac{π}{2} x) = 2

x = \frac{2 \cdot 0.72972 \dots}{π} + 4 n, x = 2 - \frac{2 \cdot 0.72972 \dots}{π} + 4 n

Solution steps

3 sin (\frac{π}{2} x) = 2

Divide both sides by

3

sin (\frac{π}{2} x) = \frac{2}{3}

Apply trig inverse properties

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

Solve

\frac{π}{2} x = arcsin (\frac{2}{3}) + 2 πn : x = \frac{2 arcsin ( \frac{2}{3} )}{π} + 4 n

Solve

\frac{π}{2} x = π - arcsin (\frac{2}{3}) + 2 πn : x = 2 - \frac{2 arcsin ( \frac{2}{3} )}{π} + 4 n

x = \frac{2 arcsin ( \frac{2}{3} )}{π} + 4 n, x = 2 - \frac{2 arcsin ( \frac{2}{3} )}{π} + 4 n

Show solutions in decimal form

x = \frac{2 \cdot 0.72972 \dots}{π} + 4 n, x = 2 - \frac{2 \cdot 0.72972 \dots}{π} + 4 n

3 cos (A) - 1 = 0

cot (\frac{x}{2}) = - 1

5 sin (\frac{2 x - π}{2}) = 0.5

16 sin^{2} (θ) = 12

tan (θ) = - \frac{57}{9}

What is the general solution for 3sin(pi/2 x)=2 ?
The general solution for 3sin(pi/2 x)=2 is x=(2*0.72972…)/pi+4n,x=2-(2*0.72972…)/pi+4n