What is the general solution for solvefor x,y=3sin(x) ?

The general solution for solvefor x,y=3sin(x) is x=arcsin(y/3)+2pin,x=pi+arcsin(-y/3)+2pin

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solvefor x,y=3sin(x)

solve for

x, y = 3 sin (x)

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

Solution steps

y = 3 sin (x)

Switch sides

3 sin (x) = y

Divide both sides by

3

3 sin (x) = y

Divide both sides by

3

\frac{3 sin ( x )}{3} = \frac{y}{3}

Simplify

sin (x) = \frac{y}{3}

sin (x) = \frac{y}{3}

Apply trig inverse properties

sin (x) = \frac{y}{3}

General solutions for

sin (x) = \frac{y}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

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

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

What is the general solution for solvefor x,y=3sin(x) ?
The general solution for solvefor x,y=3sin(x) is x=arcsin(y/3)+2pin,x=pi+arcsin(-y/3)+2pin