What is the general solution for sin(x)=(-5)/(13) ?

The general solution for sin(x)=(-5)/(13) is x=-0.39479…+2pin,x=pi+0.39479…+2pin

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sin(x)=(-5)/(13)

sin (x) = \frac{- 5}{13}

x = - 0.39479 \dots + 2 πn, x = π + 0.39479 \dots + 2 πn

Solution steps

sin (x) = \frac{- 5}{13}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

sin (x) = - \frac{5}{13}

Apply trig inverse properties

x = arcsin (- \frac{5}{13}) + 2 πn, x = π + arcsin (\frac{5}{13}) + 2 πn

Show solutions in decimal form

x = - 0.39479 \dots + 2 πn, x = π + 0.39479 \dots + 2 πn

sin^{2} (θ) - cos^{2} (θ) + cos (θ) = 0

3 sin^{2} (x) = 9 cos^{2} (x)

sin (\frac{1}{2 x}) = - 1

3 cos^{2} (x) - 3 = sin (x)

1 + cos (x) = sin^{2} (x)

What is the general solution for sin(x)=(-5)/(13) ?
The general solution for sin(x)=(-5)/(13) is x=-0.39479…+2pin,x=pi+0.39479…+2pin