What is the general solution for tan(6x)=1 ?

The general solution for tan(6x)=1 is x= pi/(24)+(pin)/6

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tan(6x)=1

tan (6 x) = 1

x = \frac{π}{24} + \frac{πn}{6}

Degrees

x = 7. 5^{\circ} + 3 0^{\circ} n

Solution steps

tan (6 x) = 1

General solutions for

tan (6 x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

6 x = \frac{π}{4} + πn

6 x = \frac{π}{4} + πn

Solve

6 x = \frac{π}{4} + πn : x = \frac{π}{24} + \frac{πn}{6}

6 x = \frac{π}{4} + πn

Divide both sides by

6

6 x = \frac{π}{4} + πn

Divide both sides by

6

\frac{6 x}{6} = \frac{\frac{π}{4}}{6} + \frac{πn}{6}

Simplify

\frac{6 x}{6} = \frac{\frac{π}{4}}{6} + \frac{πn}{6}

Simplify

\frac{6 x}{6} : x

\frac{6 x}{6}

Divide the numbers:

\frac{6}{6} = 1

= x

Simplify

\frac{\frac{π}{4}}{6} + \frac{πn}{6} : \frac{π}{24} + \frac{πn}{6}

\frac{\frac{π}{4}}{6} + \frac{πn}{6}

\frac{\frac{π}{4}}{6} = \frac{π}{24}

\frac{\frac{π}{4}}{6}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 6}

Multiply the numbers:

4 \cdot 6 = 24

= \frac{π}{24}

= \frac{π}{24} + \frac{πn}{6}

x = \frac{π}{24} + \frac{πn}{6}

x = \frac{π}{24} + \frac{πn}{6}

x = \frac{π}{24} + \frac{πn}{6}

x = \frac{π}{24} + \frac{πn}{6}

sin (2 x + 7) = cos (4 x - 7)

x, cot (x) = 2

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

2 sin (x + 6 0^{\circ}) = cos (x + 3 0^{\circ})

cot^{2} (θ) - 3 csc (θ) = - 3

What is the general solution for tan(6x)=1 ?
The general solution for tan(6x)=1 is x= pi/(24)+(pin)/6