What is the general solution for 7tan(3x)=7 ?

The general solution for 7tan(3x)=7 is x= pi/(12)+(pin)/3

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7tan(3x)=7

7 tan (3 x) = 7

x = \frac{π}{12} + \frac{πn}{3}

Degrees

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

Solution steps

7 tan (3 x) = 7

Divide both sides by

7

7 tan (3 x) = 7

Divide both sides by

7

\frac{7 tan ( 3 x )}{7} = \frac{7}{7}

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{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}

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

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \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}

sin (θ) = (\frac{0.0543}{0.9911})

sin (x) = 0.2419

(- 1 - 3 cos (x))^{2} + cos^{2} (x) = 1

tan (θ) = - \frac{19}{17}

2 sin (θ) tan (θ) - 2 sin (θ) + tan (θ) - 1 = 0

What is the general solution for 7tan(3x)=7 ?
The general solution for 7tan(3x)=7 is x= pi/(12)+(pin)/3