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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x/3)=(sqrt(3))/3

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

x = \frac{π}{2} + 3 πn

Degrees

x = 9 0^{\circ} + 54 0^{\circ} n

Solution steps

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

General solutions for

tan (\frac{x}{3}) = \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}{3} = \frac{π}{6} + πn

\frac{x}{3} = \frac{π}{6} + πn

Solve

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

\frac{x}{3} = \frac{π}{6} + πn

Multiply both sides by

3

\frac{x}{3} = \frac{π}{6} + πn

Multiply both sides by

3

\frac{3 x}{3} = 3 \cdot \frac{π}{6} + 3 πn

Simplify

\frac{3 x}{3} = 3 \cdot \frac{π}{6} + 3 πn

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

3 \cdot \frac{π}{6} + 3 πn

3 \cdot \frac{π}{6} = \frac{π}{2}

3 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 3}{6}

Cancel the common factor:

3

= \frac{π}{2}

= \frac{π}{2} + 3 πn

x = \frac{π}{2} + 3 πn

x = \frac{π}{2} + 3 πn

x = \frac{π}{2} + 3 πn

x = \frac{π}{2} + 3 πn

12 sin^{2} (x) + sin (x) - 1 = 0

2 sin^{2} (2 x) - 1 = 0

- 5 (sec (x) - 2) (2 sin (x) + 3) = 0

5 sec^{2} (x) - 5 = 0

cos (3 θ) = - \frac{1}{2}

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