What is the general solution for 2sin(x/3)+sqrt(3)=0 ?

The general solution for 2sin(x/3)+sqrt(3)=0 is x=4pi+6pin,x=5pi+6pin

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2sin(x/3)+sqrt(3)=0

2 sin (\frac{x}{3}) + 3 = 0

x = 4 π + 6 πn, x = 5 π + 6 πn

Solution steps

2 sin (\frac{x}{3}) + 3 = 0

Move

3

to the right side

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

Divide both sides by

2

sin (\frac{x}{3}) = - \frac{3}{2}

General solutions for

sin (\frac{x}{3}) = - \frac{3}{2}

\frac{x}{3} = \frac{4 π}{3} + 2 πn, \frac{x}{3} = \frac{5 π}{3} + 2 πn

Solve

\frac{x}{3} = \frac{4 π}{3} + 2 πn : x = 4 π + 6 πn

Solve

\frac{x}{3} = \frac{5 π}{3} + 2 πn : x = 5 π + 6 πn

x = 4 π + 6 πn, x = 5 π + 6 πn

tan (θ) = \frac{15}{8}

sin (θ) = 4

- 1 = cos (x) + cos (2 x)

16 arcsin (x) = 4 π

3 cos^{2} (x) - 5 cos (x) = 1 + 3 sin^{2} (x)

What is the general solution for 2sin(x/3)+sqrt(3)=0 ?
The general solution for 2sin(x/3)+sqrt(3)=0 is x=4pi+6pin,x=5pi+6pin