What is the general solution for 4tan(3x)=-4 ?

The general solution for 4tan(3x)=-4 is x= pi/4+(pin)/3

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4tan(3x)=-4

4 tan (3 x) = - 4

x = \frac{π}{4} + \frac{πn}{3}

Degrees

x = 4 5^{\circ} + 6 0^{\circ} n

Solution steps

4 tan (3 x) = - 4

Divide both sides by

4

4 tan (3 x) = - 4

Divide both sides by

4

\frac{4 tan ( 3 x )}{4} = \frac{- 4}{4}

Simplify

tan (3 x) = - 1

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{3 π}{4} + πn

3 x = \frac{3 π}{4} + πn

Solve

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

3 x = \frac{3 π}{4} + πn

Divide both sides by

3

3 x = \frac{3 π}{4} + πn

Divide both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

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

\frac{\frac{3 π}{4}}{3} = \frac{π}{4}

\frac{\frac{3 π}{4}}{3}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{3 π}{12}

Cancel the common factor:

3

= \frac{π}{4}

= \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

x = \frac{π}{4} + \frac{πn}{3}

2 sin^{2} (x) - 1 + cos (x) = 0, 0 \leq x \leq 2 π

x, arctan (x) = 4 t + c

cos (\frac{π}{3} - x) = 1

2 (cos (t))^{2} - cos (t) - 1 = 0

tan (x) = \frac{6}{15}

What is the general solution for 4tan(3x)=-4 ?
The general solution for 4tan(3x)=-4 is x= pi/4+(pin)/3