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

The general solution for tan(x)= 1/(sqrt(3)) is x= pi/6+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{6} + πn

Solution steps

tan (x) = \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 (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{π}{6} + πn

x = \frac{π}{6} + πn

sin (x) + 2 sin (x) cos (x) = 0

csc^{2} (x) - 2 = 0

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

sin (4 x) = - 2 sin (2 x)

tan (x) = - 2

What is the general solution for tan(x)= 1/(sqrt(3)) ?
The general solution for tan(x)= 1/(sqrt(3)) is x= pi/6+pin