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

Radians

x = 0.61547 \dots + 6.28318 \dots n, x = π - 0.61547 \dots + 6.28318 \dots n

Solution steps

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

Simplify

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

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

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

Apply trig inverse properties

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

General solutions for

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

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

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

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