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

The general solution for tan(3x+1)=1 is x=-1/3+pi/(12)+(pin)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(3x+1)=1

tan (3 x + 1) = 1

x = - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

Degrees

x = - 4.09859 \dots^{\circ} + 6 0^{\circ} n

Solution steps

tan (3 x + 1) = 1

General solutions for

tan (3 x + 1) = 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 + 1 = \frac{π}{4} + πn

3 x + 1 = \frac{π}{4} + πn

Solve

3 x + 1 = \frac{π}{4} + πn : x = - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

3 x + 1 = \frac{π}{4} + πn

Move

1

to the right side

3 x + 1 = \frac{π}{4} + πn

Subtract

1

from both sides

3 x + 1 - 1 = \frac{π}{4} + πn - 1

Simplify

3 x = \frac{π}{4} + πn - 1

3 x = \frac{π}{4} + πn - 1

Divide both sides by

3

3 x = \frac{π}{4} + πn - 1

Divide both sides by

3

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3} - \frac{1}{3}

Simplify

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3} - \frac{1}{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{1}{3} : - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} + \frac{πn}{3} - \frac{1}{3}

Group like terms

= - \frac{1}{3} + \frac{πn}{3} + \frac{\frac{π}{4}}{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{1}{3} + \frac{πn}{3} + \frac{π}{12}

Group like terms

= - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

x = - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

x = - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

x = - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

x = - \frac{1}{3} + \frac{π}{12} + \frac{πn}{3}

- cos (2 x) = 2 cos (2 x) - 1

sin (x) = 23

sin (A) = \frac{3}{2}

sin (θ) = \frac{3}{5}, tan (θ)

sin^{22} (x) = 0.5

What is the general solution for tan(3x+1)=1 ?
The general solution for tan(3x+1)=1 is x=-1/3+pi/(12)+(pin)/3