What is the general solution for solvefor x,2sin(5x)-1=0 ?

The general solution for solvefor x,2sin(5x)-1=0 is x= pi/(30)+(2pin)/5 ,x= pi/6+(2pin)/5

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solvefor x,2sin(5x)-1=0

solve for

x, 2 sin (5 x) - 1 = 0

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{π}{6} + \frac{2 πn}{5}

Solution steps

2 sin (5 x) - 1 = 0

Move

1

to the right side

2 sin (5 x) = 1

Divide both sides by

2

sin (5 x) = \frac{1}{2}

General solutions for

sin (5 x) = \frac{1}{2}

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

Solve

5 x = \frac{π}{6} + 2 πn : x = \frac{π}{30} + \frac{2 πn}{5}

Solve

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

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{π}{6} + \frac{2 πn}{5}

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

2 \cdot cos (2 x) + 1 = 0

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

2 sin (\frac{π x}{2}) + 1 = 0

sin (x) = 0.819

What is the general solution for solvefor x,2sin(5x)-1=0 ?
The general solution for solvefor x,2sin(5x)-1=0 is x= pi/(30)+(2pin)/5 ,x= pi/6+(2pin)/5