What is the general solution for 6sin(x)=2 ?

The general solution for 6sin(x)=2 is x=0.33983…+2pin,x=pi-0.33983…+2pin

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6sin(x)=2

6 sin (x) = 2

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

Degrees

x = 19.47122 \dots^{\circ} + 36 0^{\circ} n, x = 160.52877 \dots^{\circ} + 36 0^{\circ} n

Solution steps

6 sin (x) = 2

Divide both sides by

6

6 sin (x) = 2

Divide both sides by

6

\frac{6 sin ( x )}{6} = \frac{2}{6}

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

2 sin (x) cos (x) + 2 sin (x) = 0

4 sin (θ) = 23

sec^{2} (θ) + tan^{2} (θ) = (2)^{2}

sin (x) = 2 sin (x)

sin (2 θ) = 2 sin (θ)

What is the general solution for 6sin(x)=2 ?
The general solution for 6sin(x)=2 is x=0.33983…+2pin,x=pi-0.33983…+2pin