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

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

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

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

x = \frac{2 π}{3} + 2 πn

Degrees

x = 12 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

Add

3

to 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{π}{3} + πn

\frac{x}{2} = \frac{π}{3} + πn

Solve

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

\frac{x}{2} = \frac{π}{3} + πn

Multiply both sides by

2

\frac{x}{2} = \frac{π}{3} + πn

Multiply both sides by

2

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

Simplify

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

2 \cdot \frac{π}{3} + 2 πn

Multiply

2 \cdot \frac{π}{3} : \frac{2 π}{3}

2 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 2}{3}

= \frac{2 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn

5 sin (x) - 3 sin (3 x) = 2 sin (x)

tan (θ) = 652.70364

sec (x) + 2 = 22

2 csc^{2} (x) - 5 csc (x) + 2 = 0

x, sin (x) cos (x) = \frac{1}{2}

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