What is the general solution for tan(x-pi/6)=1 ?

The general solution for tan(x-pi/6)=1 is x=pin+(5pi)/(12)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x-pi/6)=1

Solution

tan (x - \frac{π}{6}) = 1

Solution

x = πn + \frac{5 π}{12}

Degrees

x = 7 5^{\circ} + 18 0^{\circ} n

Solution steps

tan (x - \frac{π}{6}) = 1

General solutions for

tan (x - \frac{π}{6}) = 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}

x - \frac{π}{6} = \frac{π}{4} + πn

x - \frac{π}{6} = \frac{π}{4} + πn

Solve

x - \frac{π}{6} = \frac{π}{4} + πn : x = πn + \frac{5 π}{12}

x - \frac{π}{6} = \frac{π}{4} + πn

Move

\frac{π}{6}

to the right side

x - \frac{π}{6} = \frac{π}{4} + πn

Add

\frac{π}{6}

to both sides

x - \frac{π}{6} + \frac{π}{6} = \frac{π}{4} + πn + \frac{π}{6}

Simplify

x - \frac{π}{6} + \frac{π}{6} = \frac{π}{4} + πn + \frac{π}{6}

Simplify

x - \frac{π}{6} + \frac{π}{6} : x

x - \frac{π}{6} + \frac{π}{6}

Add similar elements:

- \frac{π}{6} + \frac{π}{6} = 0

= x

Simplify

\frac{π}{4} + πn + \frac{π}{6} : πn + \frac{5 π}{12}

\frac{π}{4} + πn + \frac{π}{6}

Group like terms

= πn + \frac{π}{4} + \frac{π}{6}

Least Common Multiplier of

4, 6 : 12

4, 6

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Multiply each factor the greatest number of times it occurs in either

4

6

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

12

For

\frac{π}{4} :

multiply the denominator and numerator by

3

\frac{π}{4} = \frac{π 3}{4 \cdot 3} = \frac{π 3}{12}

For

\frac{π}{6} :

multiply the denominator and numerator by

2

\frac{π}{6} = \frac{π 2}{6 \cdot 2} = \frac{π 2}{12}

= \frac{π 3}{12} + \frac{π 2}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{π 3 + π 2}{12}

Add similar elements:

3 π + 2 π = 5 π

= πn + \frac{5 π}{12}

x = πn + \frac{5 π}{12}

x = πn + \frac{5 π}{12}

x = πn + \frac{5 π}{12}

x = πn + \frac{5 π}{12}

Popular Examples

cos^2(x)+((1-sqrt(2))/2)cos(x)-(sqrt(2))/4 =0

cos^{2} (x) + (\frac{1 - 2}{2}) cos (x) - \frac{2}{4} = 0

tan^2(x/2)=-2

tan^{2} (\frac{x}{2}) = - 2

sin^2(θ)-1=2sin(θ)

sin^{2} (θ) - 1 = 2 sin (θ)

-3sin^2(x)+2=0

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

16sin(3x)cos(x)+8sqrt(3)sin(3x)-2cos(x)-sqrt(3)=0

16 sin (3 x) cos (x) + 83 sin (3 x) - 2 cos (x) - 3 = 0

Frequently Asked Questions (FAQ)

What is the general solution for tan(x-pi/6)=1 ?
The general solution for tan(x-pi/6)=1 is x=pin+(5pi)/(12)