What is the general solution for sin(θ)=(-5)/6 ?

The general solution for sin(θ)=(-5)/6 is θ=-0.98511…+2pin,θ=pi+0.98511…+2pin

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sin(θ)=(-5)/6

sin (θ) = \frac{- 5}{6}

θ = - 0.98511 \dots + 2 πn, θ = π + 0.98511 \dots + 2 πn

Degrees

θ = - 56.44269 \dots^{\circ} + 36 0^{\circ} n, θ = 236.44269 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{- 5}{6}

Apply the fraction rule:

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

sin (θ) = - \frac{5}{6}

Apply trig inverse properties

sin (θ) = - \frac{5}{6}

General solutions for

sin (θ) = - \frac{5}{6}

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

θ = arcsin (- \frac{5}{6}) + 2 πn, θ = π + arcsin (\frac{5}{6}) + 2 πn

θ = arcsin (- \frac{5}{6}) + 2 πn, θ = π + arcsin (\frac{5}{6}) + 2 πn

Show solutions in decimal form

θ = - 0.98511 \dots + 2 πn, θ = π + 0.98511 \dots + 2 πn

\frac{sin ( x )}{16} = \frac{sin ( 3 1 ^{\circ} )}{12}

sin (A) = \frac{2}{3}

3 cos (2 x + 1) = 2

sin (t) = \frac{3}{7}, cos (t)

tan (x) = \frac{16}{12}

What is the general solution for sin(θ)=(-5)/6 ?
The general solution for sin(θ)=(-5)/6 is θ=-0.98511…+2pin,θ=pi+0.98511…+2pin