What is the general solution for 2sin(3x+1)+1=2 ?

The general solution for 2sin(3x+1)+1=2 is x=-1/3+pi/(18)+(2pin)/3 ,x=-1/3+(5pi}{18}+\frac{2pin)/3

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2sin(3x+1)+1=2

2 sin (3 x + 1) + 1 = 2

x = - \frac{1}{3} + \frac{π}{18} + \frac{2 πn}{3}, x = - \frac{1}{3} + \frac{5 π}{18} + \frac{2 πn}{3}

Solution steps

2 sin (3 x + 1) + 1 = 2

Move

1

to the right side

2 sin (3 x + 1) = 1

Divide both sides by

2

sin (3 x + 1) = \frac{1}{2}

General solutions for

sin (3 x + 1) = \frac{1}{2}

3 x + 1 = \frac{π}{6} + 2 πn, 3 x + 1 = \frac{5 π}{6} + 2 πn

Solve

3 x + 1 = \frac{π}{6} + 2 πn : x = - \frac{1}{3} + \frac{π}{18} + \frac{2 πn}{3}

Solve

3 x + 1 = \frac{5 π}{6} + 2 πn : x = - \frac{1}{3} + \frac{5 π}{18} + \frac{2 πn}{3}

x = - \frac{1}{3} + \frac{π}{18} + \frac{2 πn}{3}, x = - \frac{1}{3} + \frac{5 π}{18} + \frac{2 πn}{3}

2 sin (3 x + 1) + 1 = 1

sin (x) = 6946

sin (2 x) - \frac{3}{2} = 0, - 2 π \leq x \leq 2 π

\frac{sec ( x ) + tan ( x )}{cot ( x ) + cos ( x )} = sec^{2} (x)

cos (x) = csc (x)

What is the general solution for 2sin(3x+1)+1=2 ?
The general solution for 2sin(3x+1)+1=2 is x=-1/3+pi/(18)+(2pin)/3 ,x=-1/3+(5pi}{18}+\frac{2pin)/3