What is the general solution for sin(θ)= 9/41 ?

The general solution for sin(θ)= 9/41 is θ=0.22131…+2pin,θ=pi-0.22131…+2pin

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sin(θ)= 9/41

sin (θ) = \frac{9}{41}

θ = 0.22131 \dots + 2 πn, θ = π - 0.22131 \dots + 2 πn

Degrees

θ = 12.68038 \dots^{\circ} + 36 0^{\circ} n, θ = 167.31961 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{9}{41}

Apply trig inverse properties

sin (θ) = \frac{9}{41}

General solutions for

sin (θ) = \frac{9}{41}

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

θ = arcsin (\frac{9}{41}) + 2 πn, θ = π - arcsin (\frac{9}{41}) + 2 πn

θ = arcsin (\frac{9}{41}) + 2 πn, θ = π - arcsin (\frac{9}{41}) + 2 πn

Show solutions in decimal form

θ = 0.22131 \dots + 2 πn, θ = π - 0.22131 \dots + 2 πn

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

3 sin (θ) - cos (θ) = 1

csc (y) = 2

16 sin^{2} (θ) - 1 = 0

8 sin^{2} (x) + 16 sin (x) + 8 = 0

What is the general solution for sin(θ)= 9/41 ?
The general solution for sin(θ)= 9/41 is θ=0.22131…+2pin,θ=pi-0.22131…+2pin