What is the general solution for solvefor θ,r=2sin(θ) ?

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

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solvefor θ,r=2sin(θ)

solve for

θ, r = 2 sin (θ)

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

Solution steps

r = 2 sin (θ)

Switch sides

2 sin (θ) = r

Divide both sides by

2

2 sin (θ) = r

Divide both sides by

2

\frac{2 sin ( θ )}{2} = \frac{r}{2}

Simplify

sin (θ) = \frac{r}{2}

sin (θ) = \frac{r}{2}

Apply trig inverse properties

sin (θ) = \frac{r}{2}

General solutions for

sin (θ) = \frac{r}{2}

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

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

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

csc (3 θ) = - 1

cos (x) = 0.1234

tan (2 x) = + \frac{9}{40}

x, y = cos (6 x)

12 cos^{2} (x) - 6 sin (x) - 6 = 0 [360]

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