What is the general solution for solvefor x,3y=tan(6x) ?

The general solution for solvefor x,3y=tan(6x) is x=(arctan(3y))/6+(pin)/6

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solvefor x,3y=tan(6x)

solve for

x, 3 y = tan (6 x)

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

Solution steps

3 y = tan (6 x)

Switch sides

tan (6 x) = 3 y

Apply trig inverse properties

tan (6 x) = 3 y

General solutions for

tan (6 x) = 3 y

tan (x) = a \Rightarrow x = arctan (a) + πn

6 x = arctan (3 y) + πn

6 x = arctan (3 y) + πn

Solve

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

6 x = arctan (3 y) + πn

Divide both sides by

6

6 x = arctan (3 y) + πn

Divide both sides by

6

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

Simplify

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

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

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

3 cos (x) = sec (x)

3 csc (x) + 5 = csc (x) + 9

3 = tan^{2} (x)

tan (θ) csc (θ) + 2 tan (θ) = 0

250 = 88 sin (θ) + 242 cos (θ)

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