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

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

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5sin(x)=-4

5 sin (x) = - 4

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

Degrees

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

Solution steps

5 sin (x) = - 4

Divide both sides by

5

5 sin (x) = - 4

Divide both sides by

5

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

- π sin (π x) = 0

7 tan (4 x + 199) = 8 sin (4 x + 199)

4 sin^{2} (x) + 4 cos (x) - 5 = 0, 0 \leq x \leq 2 π

2 sin (2 θ) = 1

cos (θ) = \frac{1}{2}, 0 \leq θ \leq 4 π

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