What is the general solution for sin(θ)=-5/7 ?

The general solution for sin(θ)=-5/7 is θ=-0.79560…+2pin,θ=pi+0.79560…+2pin

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sin(θ)=-5/7

sin (θ) = - \frac{5}{7}

θ = - 0.79560 \dots + 2 πn, θ = π + 0.79560 \dots + 2 πn

Degrees

θ = - 45.58469 \dots^{\circ} + 36 0^{\circ} n, θ = 225.58469 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{5}{7}

Apply trig inverse properties

sin (θ) = - \frac{5}{7}

General solutions for

sin (θ) = - \frac{5}{7}

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

θ = arcsin (- \frac{5}{7}) + 2 πn, θ = π + arcsin (\frac{5}{7}) + 2 πn

θ = arcsin (- \frac{5}{7}) + 2 πn, θ = π + arcsin (\frac{5}{7}) + 2 πn

Show solutions in decimal form

θ = - 0.79560 \dots + 2 πn, θ = π + 0.79560 \dots + 2 πn

cos (x) sin (x) = sin (x)

sec^{2} (x) - 1 = 1

sec (θ) = 8

x, 2 cos (2 x) = 0

tan (2 θ) + tan (2 θ) sin (2 θ) = 0

What is the general solution for sin(θ)=-5/7 ?
The general solution for sin(θ)=-5/7 is θ=-0.79560…+2pin,θ=pi+0.79560…+2pin