What is the general solution for 2sin(x/5)+sqrt(3)=0 ?

The general solution for 2sin(x/5)+sqrt(3)=0 is x=(20pi)/3+10pin,x=(25pi)/3+10pin

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2sin(x/5)+sqrt(3)=0

2 sin (\frac{x}{5}) + 3 = 0

x = \frac{20 π}{3} + 10 πn, x = \frac{25 π}{3} + 10 πn

Solution steps

2 sin (\frac{x}{5}) + 3 = 0

Move

3

to the right side

2 sin (\frac{x}{5}) = - 3

Divide both sides by

2

sin (\frac{x}{5}) = - \frac{3}{2}

General solutions for

sin (\frac{x}{5}) = - \frac{3}{2}

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

Solve

\frac{x}{5} = \frac{4 π}{3} + 2 πn : x = \frac{20 π}{3} + 10 πn

Solve

\frac{x}{5} = \frac{5 π}{3} + 2 πn : x = \frac{25 π}{3} + 10 πn

x = \frac{20 π}{3} + 10 πn, x = \frac{25 π}{3} + 10 πn

sin (\frac{θ}{2}) = 1

x, z = arctan (\frac{y}{x})

4 sin^{2} (x) = 2 cos (x) + 1

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

cos^{2} (2 x + \frac{π}{6}) = \frac{1}{2}

What is the general solution for 2sin(x/5)+sqrt(3)=0 ?
The general solution for 2sin(x/5)+sqrt(3)=0 is x=(20pi)/3+10pin,x=(25pi)/3+10pin