What is the general solution for tan(-3x)=1 ?

The general solution for tan(-3x)=1 is x=-pi/(12)-(pin)/3

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tan(-3x)=1

tan (- 3 x) = 1

x = - \frac{π}{12} - \frac{πn}{3}

Degrees

x = - 1 5^{\circ} - 6 0^{\circ} n

Solution steps

tan (- 3 x) = 1

General solutions for

tan (- 3 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}

- 3 x = \frac{π}{4} + πn

- 3 x = \frac{π}{4} + πn

Solve

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

- 3 x = \frac{π}{4} + πn

Divide both sides by

- 3

- 3 x = \frac{π}{4} + πn

Divide both sides by

- 3

\frac{- 3 x}{- 3} = \frac{\frac{π}{4}}{- 3} + \frac{πn}{- 3}

Simplify

\frac{- 3 x}{- 3} = \frac{\frac{π}{4}}{- 3} + \frac{πn}{- 3}

Simplify

\frac{- 3 x}{- 3} : x

\frac{- 3 x}{- 3}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{4}}{- 3} + \frac{πn}{- 3} : - \frac{π}{12} - \frac{πn}{3}

\frac{\frac{π}{4}}{- 3} + \frac{πn}{- 3}

\frac{\frac{π}{4}}{- 3} = - \frac{π}{12}

\frac{\frac{π}{4}}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{π}{4}}{3}

Apply the fraction rule:

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

\frac{\frac{π}{4}}{3} = \frac{π}{4 \cdot 3}

= - \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= - \frac{π}{12}

= - \frac{π}{12} + \frac{πn}{- 3}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{π}{12} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}

x = - \frac{π}{12} - \frac{πn}{3}

What is the general solution for tan(-3x)=1 ?
The general solution for tan(-3x)=1 is x=-pi/(12)-(pin)/3