What is the general solution for solvefor x,y=cos(6x) ?

The general solution for solvefor x,y=cos(6x) is x=(arccos(y))/6+(pin)/3 ,x=-(arccos(y))/6+(pin)/3

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solvefor x,y=cos(6x)

solve for

x, y = cos (6 x)

x = \frac{arccos ( y )}{6} + \frac{πn}{3}, x = - \frac{arccos ( y )}{6} + \frac{πn}{3}

Solution steps

y = cos (6 x)

Switch sides

cos (6 x) = y

Apply trig inverse properties

cos (6 x) = y

General solutions for

cos (6 x) = y

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

6 x = arccos (y) + 2 πn, 6 x = - arccos (y) + 2 πn

6 x = arccos (y) + 2 πn, 6 x = - arccos (y) + 2 πn

Solve

6 x = arccos (y) + 2 πn : x = \frac{arccos ( y )}{6} + \frac{πn}{3}

6 x = arccos (y) + 2 πn

Divide both sides by

6

6 x = arccos (y) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = \frac{arccos ( y )}{6} + \frac{2 πn}{6}

Simplify

x = \frac{arccos ( y )}{6} + \frac{πn}{3}

x = \frac{arccos ( y )}{6} + \frac{πn}{3}

Solve

6 x = - arccos (y) + 2 πn : x = - \frac{arccos ( y )}{6} + \frac{πn}{3}

6 x = - arccos (y) + 2 πn

Divide both sides by

6

6 x = - arccos (y) + 2 πn

Divide both sides by

6

\frac{6 x}{6} = - \frac{arccos ( y )}{6} + \frac{2 πn}{6}

Simplify

x = - \frac{arccos ( y )}{6} + \frac{πn}{3}

x = - \frac{arccos ( y )}{6} + \frac{πn}{3}

x = \frac{arccos ( y )}{6} + \frac{πn}{3}, x = - \frac{arccos ( y )}{6} + \frac{πn}{3}

12 cos^{2} (x) - 6 sin (x) - 6 = 0 [360]

sin (θ) = - 0

tan (x) = \frac{15}{12}

6 sin (θ) + 3 sin (θ) tan (θ) = 3 sin (θ)

cos (2 x) sin (x) = 1

What is the general solution for solvefor x,y=cos(6x) ?
The general solution for solvefor x,y=cos(6x) is x=(arccos(y))/6+(pin)/3 ,x=-(arccos(y))/6+(pin)/3