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

The general solution for 2sin(5x)+3=2 is x=(7pi}{30}+(2pin)/5 ,x=(11pi)/(30)+\frac{2pin)/5

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2sin(5x)+3=2

2 sin (5 x) + 3 = 2

x = \frac{7 π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

Solution steps

2 sin (5 x) + 3 = 2

Move

3

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{7 π}{6} + 2 πn, 5 x = \frac{11 π}{6} + 2 πn

Solve

5 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{30} + \frac{2 πn}{5}

Solve

5 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{7 π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

5 sin (y) - 5 = 3 sin (y) - 4

2 cos^{2} (x) + 3 cos (x) - 3 = 0

3 sin (x) - 5 cos (x) = 0

sin^{2} (x) = 0.85

cos (x - 6 0^{\circ}) = \frac{3}{2}

What is the general solution for 2sin(5x)+3=2 ?
The general solution for 2sin(5x)+3=2 is x=(7pi}{30}+(2pin)/5 ,x=(11pi)/(30)+\frac{2pin)/5