What is the general solution for tan(x/4)+sqrt(3)=0,0<= x<= 2pi ?

The general solution for tan(x/4)+sqrt(3)=0,0<= x<= 2pi is No Solution for x\in\mathbb{R}

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tan(x/4)+sqrt(3)=0,0<= x<= 2pi

tan (\frac{x}{4}) + 3 = 0, 0 \leq x \leq 2 π

No Solution for x \in R

Solution steps

tan (\frac{x}{4}) + 3 = 0, 0 \leq x \leq 2 π

Move

3

to the right side

tan (\frac{x}{4}) + 3 = 0

Subtract

3

from both sides

tan (\frac{x}{4}) + 3 - 3 = 0 - 3

Simplify

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

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

General solutions for

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

\frac{x}{4} = \frac{2 π}{3} + πn

\frac{x}{4} = \frac{2 π}{3} + πn

Solve

\frac{x}{4} = \frac{2 π}{3} + πn : x = \frac{8 π}{3} + 4 πn

\frac{x}{4} = \frac{2 π}{3} + πn

Multiply both sides by

4

\frac{x}{4} = \frac{2 π}{3} + πn

Multiply both sides by

4

\frac{4 x}{4} = 4 \cdot \frac{2 π}{3} + 4 πn

Simplify

\frac{4 x}{4} = 4 \cdot \frac{2 π}{3} + 4 πn

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

4 \cdot \frac{2 π}{3} + 4 πn : \frac{8 π}{3} + 4 πn

4 \cdot \frac{2 π}{3} + 4 πn

4 \cdot \frac{2 π}{3} = \frac{8 π}{3}

4 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 4}{3}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{8 π}{3}

= \frac{8 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn

x = \frac{8 π}{3} + 4 πn

Solutions for the range

0 \leq x \leq 2 π

No Solution for x \in R

What is the general solution for tan(x/4)+sqrt(3)=0,0<= x<= 2pi ?
The general solution for tan(x/4)+sqrt(3)=0,0<= x<= 2pi is No Solution for x\in\mathbb{R}