What is the general solution for sin(θ)= 6/13 ?

The general solution for sin(θ)= 6/13 is θ=0.47972…+2pin,θ=pi-0.47972…+2pin

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sin(θ)= 6/13

sin (θ) = \frac{6}{13}

θ = 0.47972 \dots + 2 πn, θ = π - 0.47972 \dots + 2 πn

Degrees

θ = 27.48642 \dots^{\circ} + 36 0^{\circ} n, θ = 152.51357 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{6}{13}

Apply trig inverse properties

sin (θ) = \frac{6}{13}

General solutions for

sin (θ) = \frac{6}{13}

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

θ = arcsin (\frac{6}{13}) + 2 πn, θ = π - arcsin (\frac{6}{13}) + 2 πn

θ = arcsin (\frac{6}{13}) + 2 πn, θ = π - arcsin (\frac{6}{13}) + 2 πn

Show solutions in decimal form

θ = 0.47972 \dots + 2 πn, θ = π - 0.47972 \dots + 2 πn

2 sin (3 0^{\circ} + x) = 3 cos (x)

- 33 cot (θ) + 5 = 14

y, d = arctan (\frac{10}{\frac{y}{67} \cdot 1000})

2 arccos (x) = π

- 2 cos (θ) + 1 = 5 cos (θ) + 0

What is the general solution for sin(θ)= 6/13 ?
The general solution for sin(θ)= 6/13 is θ=0.47972…+2pin,θ=pi-0.47972…+2pin