What is the general solution for tan(x/2)+sqrt(3)=0 ?

The general solution for tan(x/2)+sqrt(3)=0 is x=(4pi)/3+2pin

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tan(x/2)+sqrt(3)=0

tan (\frac{x}{2}) + 3 = 0

x = \frac{4 π}{3} + 2 πn

Degrees

x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{x}{2}) + 3 = 0

Move

3

to the right side

tan (\frac{x}{2}) + 3 = 0

Subtract

3

from both sides

tan (\frac{x}{2}) + 3 - 3 = 0 - 3

Simplify

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

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

General solutions for

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

\frac{x}{2} = \frac{2 π}{3} + πn

Solve

\frac{x}{2} = \frac{2 π}{3} + πn : x = \frac{4 π}{3} + 2 πn

\frac{x}{2} = \frac{2 π}{3} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{2 π}{3} + πn

Multiply both sides by

2

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

Simplify

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

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

2 \cdot \frac{2 π}{3} + 2 πn : \frac{4 π}{3} + 2 πn

2 \cdot \frac{2 π}{3} + 2 πn

2 \cdot \frac{2 π}{3} = \frac{4 π}{3}

2 \cdot \frac{2 π}{3}

Multiply fractions:

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

= \frac{2 π 2}{3}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 π}{3}

= \frac{4 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn

x = \frac{4 π}{3} + 2 πn

tan^{2} (θ) - 4 = 0

csc^{2} (θ) - 2 csc (θ) - 8 = 0

(tan (θ) + 1) (cos (θ) + 1) = 0

sec (θ) = \frac{5}{3}

1 - cos (x) = 3 sin (x)

What is the general solution for tan(x/2)+sqrt(3)=0 ?
The general solution for tan(x/2)+sqrt(3)=0 is x=(4pi)/3+2pin