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

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

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sin(x)=(-4)/5

sin (x) = \frac{- 4}{5}

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

Solution steps

sin (x) = \frac{- 4}{5}

Apply the fraction rule:

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

sin (x) = - \frac{4}{5}

Apply trig inverse properties

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

Show solutions in decimal form

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

16 = 7 - 7 cos (θ)

sin (θ) = \frac{5}{4}

2 cos (x) + 2 = 0

sin (θ) = \frac{15}{17}, cos (θ)

- 5 cos^{2} (x) + 4 cos (x) + 1 = 0

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