What is the general solution for sin(θ)=-0.7659 ?

The general solution for sin(θ)=-0.7659 is θ=-0.87243…+2pin,θ=pi+0.87243…+2pin

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sin(θ)=-0.7659

sin (θ) = - 0.7659

θ = - 0.87243 \dots + 2 πn, θ = π + 0.87243 \dots + 2 πn

Degrees

θ = - 49.98712 \dots^{\circ} + 36 0^{\circ} n, θ = 229.98712 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - 0.7659

Apply trig inverse properties

sin (θ) = - 0.7659

General solutions for

sin (θ) = - 0.7659

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

θ = arcsin (- 0.7659) + 2 πn, θ = π + arcsin (0.7659) + 2 πn

θ = arcsin (- 0.7659) + 2 πn, θ = π + arcsin (0.7659) + 2 πn

Show solutions in decimal form

θ = - 0.87243 \dots + 2 πn, θ = π + 0.87243 \dots + 2 πn

4 cos (x) = - 2

3 cos^{2} (x) + cos (x) - 4 = 0

sin (θ) = 7

sin (3 x - \frac{π}{2}) = - \frac{3}{2}, (3 π, 4 π)

2 sin^{2} (x) - 7 cos (x) - 5 = 0

What is the general solution for sin(θ)=-0.7659 ?
The general solution for sin(θ)=-0.7659 is θ=-0.87243…+2pin,θ=pi+0.87243…+2pin