What is the general solution for tan(x/2)=-1/(sqrt(3)) ?

The general solution for tan(x/2)=-1/(sqrt(3)) is x=(5pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x/2)=-1/(sqrt(3))

tan (\frac{x}{2}) = - \frac{1}{3}

x = \frac{5 π}{3} + 2 πn

Solution steps

tan (\frac{x}{2}) = - \frac{1}{3}

Simplify

- \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}

tan (\frac{x}{2}) = - \frac{3}{3}

General solutions for

tan (\frac{x}{2}) = - \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}

\frac{x}{2} = \frac{5 π}{6} + πn

\frac{x}{2} = \frac{5 π}{6} + πn

Solve

\frac{x}{2} = \frac{5 π}{6} + πn : x = \frac{5 π}{3} + 2 πn

\frac{x}{2} = \frac{5 π}{6} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{5 π}{6} + πn

Multiply both sides by

2

\frac{2 x}{2} = 2 \cdot \frac{5 π}{6} + 2 πn

Simplify

\frac{2 x}{2} = 2 \cdot \frac{5 π}{6} + 2 πn

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{5 π}{6} + 2 πn : \frac{5 π}{3} + 2 πn

2 \cdot \frac{5 π}{6} + 2 πn

2 \cdot \frac{5 π}{6} = \frac{5 π}{3}

2 \cdot \frac{5 π}{6}

Multiply fractions:

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

= \frac{5 π 2}{6}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 π}{6}

Cancel the common factor:

2

= \frac{5 π}{3}

= \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

x = \frac{5 π}{3} + 2 πn

C, y = arcsin (C) e^{2}

sin (θ) = \frac{2 3}{3}

cos (x + 3 π) - cos (x) + 1 = 0

x, \frac{d ^{2} x}{d t ^{2}} + 10 sin (x) = 5

2 - 6 cos (x) = 0

What is the general solution for tan(x/2)=-1/(sqrt(3)) ?
The general solution for tan(x/2)=-1/(sqrt(3)) is x=(5pi)/3+2pin