What is the general solution for 5sin(x)=2 ?

The general solution for 5sin(x)=2 is x=0.41151…+2pin,x=pi-0.41151…+2pin

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5sin(x)=2

5 sin (x) = 2

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

Degrees

x = 23.57817 \dots^{\circ} + 36 0^{\circ} n, x = 156.42182 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 sin (x) = 2

Divide both sides by

5

5 sin (x) = 2

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{2}{5}

Simplify

sin (x) = \frac{2}{5}

sin (x) = \frac{2}{5}

Apply trig inverse properties

sin (x) = \frac{2}{5}

General solutions for

sin (x) = \frac{2}{5}

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

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

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

Show solutions in decimal form

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn

4 (cot (θ) + 1) = 2 (cot (θ) + 2)

sin (3 t) = 0

sin^{2} (x) - 3 cos (x) - 3 = 0

csc^{2} (x) = 0

1 + 2 cos (θ) = 0

What is the general solution for 5sin(x)=2 ?
The general solution for 5sin(x)=2 is x=0.41151…+2pin,x=pi-0.41151…+2pin