What is the general solution for sin(θ)=-1/5 ?

The general solution for sin(θ)=-1/5 is θ=-0.20135…+2pin,θ=pi+0.20135…+2pin

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sin(θ)=-1/5

sin (θ) = - \frac{1}{5}

θ = - 0.20135 \dots + 2 πn, θ = π + 0.20135 \dots + 2 πn

Degrees

θ = - 11.53695 \dots^{\circ} + 36 0^{\circ} n, θ = 191.53695 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = - \frac{1}{5}

Apply trig inverse properties

sin (θ) = - \frac{1}{5}

General solutions for

sin (θ) = - \frac{1}{5}

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

θ = arcsin (- \frac{1}{5}) + 2 πn, θ = π + arcsin (\frac{1}{5}) + 2 πn

θ = arcsin (- \frac{1}{5}) + 2 πn, θ = π + arcsin (\frac{1}{5}) + 2 πn

Show solutions in decimal form

θ = - 0.20135 \dots + 2 πn, θ = π + 0.20135 \dots + 2 πn

5 cot (x) - 5 = 0

2 - \frac{1}{2} sin (3 x + 330) = \frac{8 - 3}{4}

2 sin^{2} (x) + sin (x) + 1 = 0

sin (x) = \frac{20}{29}

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

What is the general solution for sin(θ)=-1/5 ?
The general solution for sin(θ)=-1/5 is θ=-0.20135…+2pin,θ=pi+0.20135…+2pin