en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(3x)=1,-2pi<= x<= 2pi

Solution

tan (3 x) = 1, - 2 π \leq x \leq 2 π

Solution

x = \frac{π}{12}, x = \frac{5 π}{12}, x = \frac{3 π}{4}, x = \frac{13 π}{12}, x = \frac{17 π}{12}, x = - \frac{π}{4}, x = - \frac{7 π}{12}, x = - \frac{11 π}{12}, x = - \frac{5 π}{4}

+1

Degrees

x = 1 5^{\circ}, x = 7 5^{\circ}, x = 13 5^{\circ}, x = 19 5^{\circ}, x = 25 5^{\circ}, x = - 4 5^{\circ}, x = - 10 5^{\circ}, x = - 16 5^{\circ}, x = - 22 5^{\circ}

Solution steps

tan (3 x) = 1, - 2 π \leq x \leq 2 π

General solutions for

tan (3 x) = 1

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}

3 x = \frac{π}{4} + πn

3 x = \frac{π}{4} + πn

Solve

3 x = \frac{π}{4} + πn : x = \frac{π}{12} + \frac{πn}{3}

3 x = \frac{π}{4} + πn

Divide both sides by

3

3 x = \frac{π}{4} + πn

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{\frac{π}{4}}{3} + \frac{πn}{3} : \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

Solutions for the range

- 2 π \leq x \leq 2 π

x = \frac{π}{12}, x = \frac{5 π}{12}, x = \frac{3 π}{4}, x = \frac{13 π}{12}, x = \frac{17 π}{12}, x = - \frac{π}{4}, x = - \frac{7 π}{12}, x = - \frac{11 π}{12}, x = - \frac{5 π}{4}

Popular Examples

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

cos(x)sin(2x)+3sin^2(x)=-3sin(x)

cos (x) sin (2 x) + 3 sin^{2} (x) = - 3 sin (x)

sin^2(x)=-cos(x)

sin^{2} (x) = - cos (x)

arctan(x)= pi/(12)

arctan (x) = \frac{π}{12}

8sin^2(w)+10sin(w)+3=0

8 sin^{2} (w) + 10 sin (w) + 3 = 0