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 the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

2 csc (θ) + 3 sec (θ) = 0

6 + 9 cos (x) = 2 sin^{2} (x)

tan (2 θ) = \frac{77}{51 - 20}

2 - 7 cos (x) = 0

cos (θ) = - \frac{8}{17}

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