What is the general solution for sin(θ)=-8/17 ?

The general solution for sin(θ)=-8/17 is θ=-0.48995…+2pin,θ=pi+0.48995…+2pin

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sin(θ)=-8/17

sin (θ) = - \frac{8}{17}

θ = - 0.48995 \dots + 2 πn, θ = π + 0.48995 \dots + 2 πn

Degrees

θ = - 28.07248 \dots^{\circ} + 36 0^{\circ} n, θ = 208.07248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{8}{17}

Apply trig inverse properties

sin (θ) = - \frac{8}{17}

General solutions for

sin (θ) = - \frac{8}{17}

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

θ = arcsin (- \frac{8}{17}) + 2 πn, θ = π + arcsin (\frac{8}{17}) + 2 πn

θ = arcsin (- \frac{8}{17}) + 2 πn, θ = π + arcsin (\frac{8}{17}) + 2 πn

Show solutions in decimal form

θ = - 0.48995 \dots + 2 πn, θ = π + 0.48995 \dots + 2 πn

sin (\frac{θ}{2}) - cos (θ) = 0

12 sec^{2} (x) - 16 = 0

cos (3 x - \frac{π}{8}) = \frac{2}{2}

5 (1 - cos (θ)) = sin^{2} (θ)

tan (x) - sec (x) = 1

What is the general solution for sin(θ)=-8/17 ?
The general solution for sin(θ)=-8/17 is θ=-0.48995…+2pin,θ=pi+0.48995…+2pin