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 = 211.00271 \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

- 2 sin (x) = - 2

sin (π - x) = cos (\frac{3 π}{2} - x) + cos (π)

4 csc (x) + 8 = 0

2 cos (2 θ) + 3 = 2

sin (\frac{3 π}{2} - 2 x) = sin (x)

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