What is the general solution for 4sqrt(3)tan(x)+4=0 ?

The general solution for 4sqrt(3)tan(x)+4=0 is x=(5pi)/6+pin

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4sqrt(3)tan(x)+4=0

43 tan (x) + 4 = 0

x = \frac{5 π}{6} + πn

Degrees

x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

43 tan (x) + 4 = 0

Move

4

to the right side

43 tan (x) + 4 = 0

Subtract

4

from both sides

43 tan (x) + 4 - 4 = 0 - 4

Simplify

43 tan (x) = - 4

43 tan (x) = - 4

Divide both sides by

43

43 tan (x) = - 4

Divide both sides by

43

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

Simplify

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

Simplify

\frac{4 3 tan ( x )}{4 3} : tan (x)

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

Divide the numbers:

\frac{4}{4} = 1

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

Cancel the common factor:

3

= tan (x)

Simplify

\frac{- 4}{4 3} : - \frac{3}{3}

\frac{- 4}{4 3}

Apply the fraction rule:

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

= - \frac{4}{4 3}

Divide the numbers:

\frac{4}{4} = 1

= - \frac{1}{3}

Rationalize

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

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

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

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

General solutions for

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

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

- 2 cos (a) + 6 = cos (a) + 9

sin (θ) = 0.64

tan (θ) = \frac{6}{5}

sin (2 x) = 2 cos (x), 0 \leq x \leq 2 π

y, x = arccos (y)

What is the general solution for 4sqrt(3)tan(x)+4=0 ?
The general solution for 4sqrt(3)tan(x)+4=0 is x=(5pi)/6+pin