What is the general solution for 2cos(3x+pi/2)=-1 ?

The general solution for 2cos(3x+pi/2)=-1 is x=(2pin)/3+pi/(18),x=(2pin)/3+(5pi)/(18)

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2cos(3x+pi/2)=-1

2 cos (3 x + \frac{π}{2}) = - 1

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

Solution steps

2 cos (3 x + \frac{π}{2}) = - 1

Divide both sides by

2

cos (3 x + \frac{π}{2}) = - \frac{1}{2}

General solutions for

cos (3 x + \frac{π}{2}) = - \frac{1}{2}

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

Solve

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

Solve

3 x + \frac{π}{2} = \frac{4 π}{3} + 2 πn : x = \frac{2 πn}{3} + \frac{5 π}{18}

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

sin (\frac{3 θ}{2}) = 0

4 sin (\frac{π}{2} x) = 3

1 + cos (θ) = 2 cos (θ)

2 sin (x) cos (x) = - cos (x)

tan (2 t) = 0

What is the general solution for 2cos(3x+pi/2)=-1 ?
The general solution for 2cos(3x+pi/2)=-1 is x=(2pin)/3+pi/(18),x=(2pin)/3+(5pi)/(18)