What is the general solution for sin(θ)= 3/10 ?

The general solution for sin(θ)= 3/10 is θ=0.30469…+2pin,θ=pi-0.30469…+2pin

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sin(θ)= 3/10

sin (θ) = \frac{3}{10}

θ = 0.30469 \dots + 2 πn, θ = π - 0.30469 \dots + 2 πn

Degrees

θ = 17.45760 \dots^{\circ} + 36 0^{\circ} n, θ = 162.54239 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{3}{10}

Apply trig inverse properties

sin (θ) = \frac{3}{10}

General solutions for

sin (θ) = \frac{3}{10}

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

θ = arcsin (\frac{3}{10}) + 2 πn, θ = π - arcsin (\frac{3}{10}) + 2 πn

θ = arcsin (\frac{3}{10}) + 2 πn, θ = π - arcsin (\frac{3}{10}) + 2 πn

Show solutions in decimal form

θ = 0.30469 \dots + 2 πn, θ = π - 0.30469 \dots + 2 πn

30 arctan (x) = 5 π

cosh (2 x) - 10 cosh (x) + 13 = 0

3 sin (x) - sin (2 x) = 0

7 cos^{2} (x) + 14 cos (x) + 7 = 0

θ, 2 sin (θ) = 2 cos (2 θ)

What is the general solution for sin(θ)= 3/10 ?
The general solution for sin(θ)= 3/10 is θ=0.30469…+2pin,θ=pi-0.30469…+2pin