What is the general solution for sin(θ)=(-12)/(13) ?

The general solution for sin(θ)=(-12)/(13) is θ=-1.17600…+2pin,θ=pi+1.17600…+2pin

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sin(θ)=(-12)/(13)

sin (θ) = \frac{- 12}{13}

θ = - 1.17600 \dots + 2 πn, θ = π + 1.17600 \dots + 2 πn

Degrees

θ = - 67.38013 \dots^{\circ} + 36 0^{\circ} n, θ = 247.38013 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{- 12}{13}

Apply the fraction rule:

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

sin (θ) = - \frac{12}{13}

Apply trig inverse properties

sin (θ) = - \frac{12}{13}

General solutions for

sin (θ) = - \frac{12}{13}

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

θ = arcsin (- \frac{12}{13}) + 2 πn, θ = π + arcsin (\frac{12}{13}) + 2 πn

θ = arcsin (- \frac{12}{13}) + 2 πn, θ = π + arcsin (\frac{12}{13}) + 2 πn

Show solutions in decimal form

θ = - 1.17600 \dots + 2 πn, θ = π + 1.17600 \dots + 2 πn

tan (x) = (\frac{3}{4})

50 = 25 sin (\frac{π}{2} (x + 1)) + 40

4 sin (2 x) = 0, - π \leq x \leq π

cos (x) = - 0.6987

sin (2 x) = \frac{( 2 m - 3 )}{3}

What is the general solution for sin(θ)=(-12)/(13) ?
The general solution for sin(θ)=(-12)/(13) is θ=-1.17600…+2pin,θ=pi+1.17600…+2pin