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

The general solution for 2cos(3x)+sqrt(2)=0 is x= pi/4+(2pin)/3 ,x=(5pi}{12}+\frac{2pin)/3

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2cos(3x)+sqrt(2)=0

2 cos (3 x) + 2 = 0

x = \frac{π}{4} + \frac{2 πn}{3}, x = \frac{5 π}{12} + \frac{2 πn}{3}

Solution steps

2 cos (3 x) + 2 = 0

Move

2

to the right side

2 cos (3 x) = - 2

Divide both sides by

2

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

General solutions for

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

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

Solve

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

Solve

3 x = \frac{5 π}{4} + 2 πn : x = \frac{5 π}{12} + \frac{2 πn}{3}

x = \frac{π}{4} + \frac{2 πn}{3}, x = \frac{5 π}{12} + \frac{2 πn}{3}

cos (2 x) - sin (- x) = 0

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

sin (θ) - 2 sin (θ) cos (θ) = 0

6 cos^{2} (x) + cos (2 x) = 1

sin (2 π t) = 1

What is the general solution for 2cos(3x)+sqrt(2)=0 ?
The general solution for 2cos(3x)+sqrt(2)=0 is x= pi/4+(2pin)/3 ,x=(5pi}{12}+\frac{2pin)/3