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 = 126.86989 \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

5 sin (x) = 3

sin (x) (2 cos (x) - 3) = 0

cos^{2} (x) + 5 cos (x) = cos (x) - 3

- 9 sin (x) - 9 cos (x) = 0

cot (x) = \frac{1}{3}

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