What is the general solution for tan(5x)+sqrt(3)=0 ?

The general solution for tan(5x)+sqrt(3)=0 is x=(2pi}{15}+\frac{pin)/5

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tan(5x)+sqrt(3)=0

tan (5 x) + 3 = 0

x = \frac{2 π}{15} + \frac{πn}{5}

Degrees

x = 2 4^{\circ} + 3 6^{\circ} n

Solution steps

tan (5 x) + 3 = 0

Move

3

to the right side

tan (5 x) + 3 = 0

Subtract

3

from both sides

tan (5 x) + 3 - 3 = 0 - 3

Simplify

tan (5 x) = - 3

tan (5 x) = - 3

General solutions for

tan (5 x) = - 3

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}

5 x = \frac{2 π}{3} + πn

5 x = \frac{2 π}{3} + πn

Solve

5 x = \frac{2 π}{3} + πn : x = \frac{2 π}{15} + \frac{πn}{5}

5 x = \frac{2 π}{3} + πn

Divide both sides by

5

5 x = \frac{2 π}{3} + πn

Divide both sides by

5

\frac{5 x}{5} = \frac{\frac{2 π}{3}}{5} + \frac{πn}{5}

Simplify

\frac{5 x}{5} = \frac{\frac{2 π}{3}}{5} + \frac{πn}{5}

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

\frac{\frac{2 π}{3}}{5} + \frac{πn}{5} : \frac{2 π}{15} + \frac{πn}{5}

\frac{\frac{2 π}{3}}{5} + \frac{πn}{5}

\frac{\frac{2 π}{3}}{5} = \frac{2 π}{15}

\frac{\frac{2 π}{3}}{5}

Apply the fraction rule:

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

= \frac{2 π}{3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{2 π}{15}

= \frac{2 π}{15} + \frac{πn}{5}

x = \frac{2 π}{15} + \frac{πn}{5}

x = \frac{2 π}{15} + \frac{πn}{5}

x = \frac{2 π}{15} + \frac{πn}{5}

x = \frac{2 π}{15} + \frac{πn}{5}

2 tan (x) sin (x) - 7 sin (x) = 0

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

- 3 sin^{2} (θ) + 3 = - 10 cos (θ) - 3

cos (2 x) + 2 sin (x) = 1

cot (3 x) = \frac{3}{3}

What is the general solution for tan(5x)+sqrt(3)=0 ?
The general solution for tan(5x)+sqrt(3)=0 is x=(2pi}{15}+\frac{pin)/5