What is the general solution for tan(x)= 1/(sqrt(3)),0<= x<2pi ?

The general solution for tan(x)= 1/(sqrt(3)),0<= x<2pi is x= pi/6 ,x=(7pi)/6

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)),0<= x<2pi

tan (x) = \frac{1}{3}, 0 \leq x < 2 π

x = \frac{π}{6}, x = \frac{7 π}{6}

Solution steps

tan (x) = \frac{1}{3}, 0 \leq x < 2 π

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

Solutions for the range

0 \leq x < 2 π

x = \frac{π}{6}, x = \frac{7 π}{6}

- 2 sin (2 x) = 2 π

arccos (θ) = \frac{17}{18}

cos (θ) = - \frac{2}{9}

y = sin (x), x

5 sin (y) cos (y) = 2

What is the general solution for tan(x)= 1/(sqrt(3)),0<= x<2pi ?
The general solution for tan(x)= 1/(sqrt(3)),0<= x<2pi is x= pi/6 ,x=(7pi)/6