What is the general solution for tan(x/7)+sqrt(3)=0 ?

The general solution for tan(x/7)+sqrt(3)=0 is x=(14pi)/3+7pin

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tan(x/7)+sqrt(3)=0

tan (\frac{x}{7}) + 3 = 0

x = \frac{14 π}{3} + 7 πn

Degrees

x = 84 0^{\circ} + 126 0^{\circ} n

Solution steps

tan (\frac{x}{7}) + 3 = 0

Move

3

to the right side

tan (\frac{x}{7}) + 3 = 0

Subtract

3

from both sides

tan (\frac{x}{7}) + 3 - 3 = 0 - 3

Simplify

tan (\frac{x}{7}) = - 3

tan (\frac{x}{7}) = - 3

General solutions for

tan (\frac{x}{7}) = - 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}{7} = \frac{2 π}{3} + πn

\frac{x}{7} = \frac{2 π}{3} + πn

Solve

\frac{x}{7} = \frac{2 π}{3} + πn : x = \frac{14 π}{3} + 7 πn

\frac{x}{7} = \frac{2 π}{3} + πn

Multiply both sides by

7

\frac{x}{7} = \frac{2 π}{3} + πn

Multiply both sides by

7

\frac{7 x}{7} = 7 \cdot \frac{2 π}{3} + 7 πn

Simplify

\frac{7 x}{7} = 7 \cdot \frac{2 π}{3} + 7 πn

Simplify

\frac{7 x}{7} : x

\frac{7 x}{7}

Divide the numbers:

\frac{7}{7} = 1

= x

Simplify

7 \cdot \frac{2 π}{3} + 7 πn : \frac{14 π}{3} + 7 πn

7 \cdot \frac{2 π}{3} + 7 πn

7 \cdot \frac{2 π}{3} = \frac{14 π}{3}

7 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 7}{3}

Multiply the numbers:

2 \cdot 7 = 14

= \frac{14 π}{3}

= \frac{14 π}{3} + 7 πn

x = \frac{14 π}{3} + 7 πn

x = \frac{14 π}{3} + 7 πn

x = \frac{14 π}{3} + 7 πn

x = \frac{14 π}{3} + 7 πn

3 (tan (θ) - 2) = 2 tan (θ) - 7

3 tan (θ) + 1 = 0, 0 \leq θ \leq 2 π

tan (x) = tan^{2} (x)

y, sin (x y) = x

tan (x) sec (x) = tan (x)

What is the general solution for tan(x/7)+sqrt(3)=0 ?
The general solution for tan(x/7)+sqrt(3)=0 is x=(14pi)/3+7pin