What is the general solution for 2cos(3x)+1=0 ?

The general solution for 2cos(3x)+1=0 is x=(2pi)/9+(2pin)/3 ,x=(4pi)/9+(2pin)/3

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2cos(3x)+1=0

2 cos (3 x) + 1 = 0

x = \frac{2 π}{9} + \frac{2 πn}{3}, x = \frac{4 π}{9} + \frac{2 πn}{3}

Solution steps

2 cos (3 x) + 1 = 0

Move

1

to the right side

2 cos (3 x) = - 1

Divide both sides by

2

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

General solutions for

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

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

Solve

3 x = \frac{2 π}{3} + 2 πn : x = \frac{2 π}{9} + \frac{2 πn}{3}

Solve

3 x = \frac{4 π}{3} + 2 πn : x = \frac{4 π}{9} + \frac{2 πn}{3}

x = \frac{2 π}{9} + \frac{2 πn}{3}, x = \frac{4 π}{9} + \frac{2 πn}{3}

4 cos^{2} (x) - 3 = 0, 0 \leq x \leq 2 π

3 cos (x) + 3 = 2 sin^{2} (x)

- 4 cos (x) = - sin^{2} (x) + 1

12 cos^{2} (x) - 9 = 0

sin^{4} (x) + cos^{4} (x) = 1

What is the general solution for 2cos(3x)+1=0 ?
The general solution for 2cos(3x)+1=0 is x=(2pi)/9+(2pin)/3 ,x=(4pi)/9+(2pin)/3