What is the general solution for sin(x)= 1/(sqrt(3)) ?

The general solution for sin(x)= 1/(sqrt(3)) is x=0.61547…+2pin,x=pi-0.61547…+2pin

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sin(x)= 1/(sqrt(3))

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

x = 0.61547 \dots + 2 πn, x = π - 0.61547 \dots + 2 πn

Solution steps

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

Simplify

\frac{1}{3} : \frac{3}{3}

Apply trig inverse properties

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

Show solutions in decimal form

x = 0.61547 \dots + 2 πn, x = π - 0.61547 \dots + 2 πn

2 sin^{2} (x) + 9 cos (x) = 6

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

tan^{2} (x) - sec^{2} (x) = 1

sin (x) = - sin (x)

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

What is the general solution for sin(x)= 1/(sqrt(3)) ?
The general solution for sin(x)= 1/(sqrt(3)) is x=0.61547…+2pin,x=pi-0.61547…+2pin