What is the general solution for -8sin(θ)=-3 ?

The general solution for -8sin(θ)=-3 is θ=0.38439…+2pin,θ=pi-0.38439…+2pin

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-8sin(θ)=-3

- 8 sin (θ) = - 3

θ = 0.38439 \dots + 2 πn, θ = π - 0.38439 \dots + 2 πn

Degrees

θ = 22.02431 \dots^{\circ} + 36 0^{\circ} n, θ = 157.97568 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 8 sin (θ) = - 3

Divide both sides by

- 8

- 8 sin (θ) = - 3

Divide both sides by

- 8

\frac{- 8 sin ( θ )}{- 8} = \frac{- 3}{- 8}

Simplify

sin (θ) = \frac{3}{8}

sin (θ) = \frac{3}{8}

Apply trig inverse properties

sin (θ) = \frac{3}{8}

General solutions for

sin (θ) = \frac{3}{8}

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

θ = arcsin (\frac{3}{8}) + 2 πn, θ = π - arcsin (\frac{3}{8}) + 2 πn

θ = arcsin (\frac{3}{8}) + 2 πn, θ = π - arcsin (\frac{3}{8}) + 2 πn

Show solutions in decimal form

θ = 0.38439 \dots + 2 πn, θ = π - 0.38439 \dots + 2 πn

sin (x) + 1 = 1

- 12 cot (x) - 43 = 0

3 sin^{2} (t) = 2 cos (t) sin (t)

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) = 0

cos (x) (tan (x) + \frac{cos ( x )}{sin ( x )}) = 2

What is the general solution for -8sin(θ)=-3 ?
The general solution for -8sin(θ)=-3 is θ=0.38439…+2pin,θ=pi-0.38439…+2pin