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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(θ)= 3/(sqrt(3))

tan (θ) = \frac{3}{3}

θ = \frac{π}{3} + πn

Solution steps

tan (θ) = \frac{3}{3}

Simplify

\frac{3}{3} : 3

\frac{3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 3^{\frac{1}{2}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= 3

General solutions for

tan (θ) = 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}

θ = \frac{π}{3} + πn

θ = \frac{π}{3} + πn

2 sin (3 x) + 2 = 4

sin (4 x) - 2 sin (2 x) = 0

43 tan (x) + 4 = 0

- 2 cos (a) + 6 = cos (a) + 9

sin (θ) = 0.64

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