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

The general solution for 2sin(5x)+sqrt(3)=0 is x=(4pi}{15}+\frac{2pin)/5 ,x= pi/3+(2pin)/5

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

2 sin (5 x) + 3 = 0

x = \frac{4 π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Solution steps

2 sin (5 x) + 3 = 0

Move

3

to the right side

2 sin (5 x) = - 3

Divide both sides by

2

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

General solutions for

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

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

Solve

5 x = \frac{4 π}{3} + 2 πn : x = \frac{4 π}{15} + \frac{2 πn}{5}

Solve

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

x = \frac{4 π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

cot^{2} (x) + 2 csc (x) = - 1

3 cos (θ) - 1 = 0

2 cos^{2} (θ) - cos (θ) = 0

cos^{2} (x) + cos (x) - 2 = 0

cos (x) = \frac{1}{2}

What is the general solution for 2sin(5x)+sqrt(3)=0 ?
The general solution for 2sin(5x)+sqrt(3)=0 is x=(4pi}{15}+\frac{2pin)/5 ,x= pi/3+(2pin)/5