What is the general solution for sin(θ)=(sqrt(13))/7 ?

The general solution for sin(θ)=(sqrt(13))/7 is θ=0.54109…+2pin,θ=pi-0.54109…+2pin

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sin(θ)=(sqrt(13))/7

sin (θ) = \frac{13}{7}

θ = 0.54109 \dots + 2 πn, θ = π - 0.54109 \dots + 2 πn

Degrees

θ = 31.00271 \dots^{\circ} + 36 0^{\circ} n, θ = 148.99728 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{13}{7}

Apply trig inverse properties

sin (θ) = \frac{13}{7}

General solutions for

sin (θ) = \frac{13}{7}

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

θ = arcsin (\frac{13}{7}) + 2 πn, θ = π - arcsin (\frac{13}{7}) + 2 πn

θ = arcsin (\frac{13}{7}) + 2 πn, θ = π - arcsin (\frac{13}{7}) + 2 πn

Show solutions in decimal form

θ = 0.54109 \dots + 2 πn, θ = π - 0.54109 \dots + 2 πn

sin^{2} (θ) - cos^{2} (θ) = 1

2 sin (3 θ) = 2

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

(cot (x) + 1) (3 cot (x) + 1) = 0

3 sin (θ) = - cos (θ)

What is the general solution for sin(θ)=(sqrt(13))/7 ?
The general solution for sin(θ)=(sqrt(13))/7 is θ=0.54109…+2pin,θ=pi-0.54109…+2pin