What is the general solution for sin(θ)=-12/13 ?

The general solution for sin(θ)=-12/13 is θ=-1.17600…+2pin,θ=pi+1.17600…+2pin

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sin(θ)=-12/13

sin (θ) = - \frac{12}{13}

θ = - 1.17600 \dots + 2 πn, θ = π + 1.17600 \dots + 2 πn

Degrees

θ = - 67.38013 \dots^{\circ} + 36 0^{\circ} n, θ = 247.38013 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{12}{13}

Apply trig inverse properties

sin (θ) = - \frac{12}{13}

General solutions for

sin (θ) = - \frac{12}{13}

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

θ = arcsin (- \frac{12}{13}) + 2 πn, θ = π + arcsin (\frac{12}{13}) + 2 πn

θ = arcsin (- \frac{12}{13}) + 2 πn, θ = π + arcsin (\frac{12}{13}) + 2 πn

Show solutions in decimal form

θ = - 1.17600 \dots + 2 πn, θ = π + 1.17600 \dots + 2 πn

sin (x) cos (x) = - \frac{1}{4}

sec^{2} (θ) - 9 = 0

2 cos^{2} (θ) = 2 - sin (θ)

cos (x + 1) = 0

sec^{2} (x) + tan^{2} (x) = 7

What is the general solution for sin(θ)=-12/13 ?
The general solution for sin(θ)=-12/13 is θ=-1.17600…+2pin,θ=pi+1.17600…+2pin