What is the general solution for tan((x+pi)/6)=sqrt(3) ?

The general solution for tan((x+pi)/6)=sqrt(3) is x=pi+6pin

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tan((x+pi)/6)=sqrt(3)

tan (\frac{x + π}{6}) = 3

x = π + 6 πn

Degrees

x = 18 0^{\circ} + 108 0^{\circ} n

Solution steps

tan (\frac{x + π}{6}) = 3

General solutions for

tan (\frac{x + π}{6}) = 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}

\frac{x + π}{6} = \frac{π}{3} + πn

\frac{x + π}{6} = \frac{π}{3} + πn

Solve

\frac{x + π}{6} = \frac{π}{3} + πn : x = π + 6 πn

\frac{x + π}{6} = \frac{π}{3} + πn

Multiply both sides by

6

\frac{x + π}{6} = \frac{π}{3} + πn

Multiply both sides by

6

\frac{6 ( x + π )}{6} = 6 \cdot \frac{π}{3} + 6 πn

Simplify

\frac{6 ( x + π )}{6} = 6 \cdot \frac{π}{3} + 6 πn

Simplify

\frac{6 ( x + π )}{6} : x + π

\frac{6 ( x + π )}{6}

Divide the numbers:

\frac{6}{6} = 1

= x + π

Simplify

6 \cdot \frac{π}{3} + 6 πn : 2 π + 6 πn

6 \cdot \frac{π}{3} + 6 πn

6 \cdot \frac{π}{3} = 2 π

6 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2 π

= 2 π + 6 πn

x + π = 2 π + 6 πn

x + π = 2 π + 6 πn

x + π = 2 π + 6 πn

Move

π

to the right side

x + π = 2 π + 6 πn

Subtract

π

from both sides

x + π - π = 2 π + 6 πn - π

Simplify

x = π + 6 πn

x = π + 6 πn

x = π + 6 πn

tan (x) = \frac{- 1}{2}

tan (x) = \frac{- 1}{3}

sin (x) = \frac{4}{11}

7 sin (\frac{π}{3} x) = 2

cos (x) = 0.64

What is the general solution for tan((x+pi)/6)=sqrt(3) ?
The general solution for tan((x+pi)/6)=sqrt(3) is x=pi+6pin