What is the general solution for sin(θ)=(-4)/5 ?

The general solution for sin(θ)=(-4)/5 is θ=-0.92729…+2pin,θ=pi+0.92729…+2pin

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sin(θ)=(-4)/5

sin (θ) = \frac{- 4}{5}

θ = - 0.92729 \dots + 2 πn, θ = π + 0.92729 \dots + 2 πn

Degrees

θ = - 53.13010 \dots^{\circ} + 36 0^{\circ} n, θ = 233.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{- 4}{5}

Apply the fraction rule:

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

sin (θ) = - \frac{4}{5}

Apply trig inverse properties

sin (θ) = - \frac{4}{5}

General solutions for

sin (θ) = - \frac{4}{5}

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

θ = arcsin (- \frac{4}{5}) + 2 πn, θ = π + arcsin (\frac{4}{5}) + 2 πn

θ = arcsin (- \frac{4}{5}) + 2 πn, θ = π + arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

θ = - 0.92729 \dots + 2 πn, θ = π + 0.92729 \dots + 2 πn

θ, x = 5 sec (θ)

sec (3 x) - cos (3 0^{\circ}) = 0, \frac{x + 35}{5}

- 2 sin (x) + 3 = 0

sin (θ) = \frac{4}{5}, cos (θ) = \frac{3}{5}

sec (2 x) + tan (2 x) = 8

What is the general solution for sin(θ)=(-4)/5 ?
The general solution for sin(θ)=(-4)/5 is θ=-0.92729…+2pin,θ=pi+0.92729…+2pin