What is the general solution for cos(3y)=-1/(sqrt(2)) ?

The general solution for cos(3y)=-1/(sqrt(2)) is y= pi/4+(2pin)/3 ,y=(5pi}{12}+\frac{2pin)/3

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cos(3y)=-1/(sqrt(2))

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

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

Solution steps

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

Simplify

- \frac{1}{2} : - \frac{2}{2}

General solutions for

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

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

Solve

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

Solve

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

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

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

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

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

7 (1 - cos (θ)) = sin^{2} (θ)

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

What is the general solution for cos(3y)=-1/(sqrt(2)) ?
The general solution for cos(3y)=-1/(sqrt(2)) is y= pi/4+(2pin)/3 ,y=(5pi}{12}+\frac{2pin)/3