What is the general solution for solvefor θ,y=4sin(θ) ?

The general solution for solvefor θ,y=4sin(θ) is θ=arcsin(y/4)+2pin,θ=pi+arcsin(-y/4)+2pin

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solvefor θ,y=4sin(θ)

solvefor

θ = arcsin (\frac{y}{4}) + 2 πn, θ = π + arcsin (- \frac{y}{4}) + 2 πn

Solution steps

y = 4 sin (θ)

Switch sides

4 sin (θ) = y

Divide both sides by

4

4 sin (θ) = y

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{y}{4}

Simplify

sin (θ) = \frac{y}{4}

sin (θ) = \frac{y}{4}

Apply trig inverse properties

sin (θ) = \frac{y}{4}

General solutions for

sin (θ) = \frac{y}{4}

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

θ = arcsin (\frac{y}{4}) + 2 πn, θ = π + arcsin (- \frac{y}{4}) + 2 πn

θ = arcsin (\frac{y}{4}) + 2 πn, θ = π + arcsin (- \frac{y}{4}) + 2 πn

What is the general solution for solvefor θ,y=4sin(θ) ?
The general solution for solvefor θ,y=4sin(θ) is θ=arcsin(y/4)+2pin,θ=pi+arcsin(-y/4)+2pin