What is the general solution for sin(θ)=-3/4 ?

The general solution for sin(θ)=-3/4 is θ=-0.84806…+2pin,θ=pi+0.84806…+2pin

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sin(θ)=-3/4

sin (θ) = - \frac{3}{4}

θ = - 0.84806 \dots + 2 πn, θ = π + 0.84806 \dots + 2 πn

Degrees

θ = - 48.59037 \dots^{\circ} + 36 0^{\circ} n, θ = 228.59037 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{3}{4}

Apply trig inverse properties

sin (θ) = - \frac{3}{4}

General solutions for

sin (θ) = - \frac{3}{4}

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

θ = arcsin (- \frac{3}{4}) + 2 πn, θ = π + arcsin (\frac{3}{4}) + 2 πn

θ = arcsin (- \frac{3}{4}) + 2 πn, θ = π + arcsin (\frac{3}{4}) + 2 πn

Show solutions in decimal form

θ = - 0.84806 \dots + 2 πn, θ = π + 0.84806 \dots + 2 πn

4 cos^{2} (θ) - 4 cos (θ) + 1 = 0

3 sin (x) = 3 cos (x)

y, x = - 3 ∣ sin (y) ∣

tan (x) - cot (x) = 0

1 = tan (x)

What is the general solution for sin(θ)=-3/4 ?
The general solution for sin(θ)=-3/4 is θ=-0.84806…+2pin,θ=pi+0.84806…+2pin