What is the general solution for 3tan(x/4)-sqrt(3)=0 ?

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

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3tan(x/4)-sqrt(3)=0

3 tan (\frac{x}{4}) - 3 = 0

x = \frac{2 π}{3} + 4 πn

Degrees

x = 12 0^{\circ} + 72 0^{\circ} n

Solution steps

3 tan (\frac{x}{4}) - 3 = 0

Move

3

to the right side

3 tan (\frac{x}{4}) - 3 = 0

Add

3

to both sides

3 tan (\frac{x}{4}) - 3 + 3 = 0 + 3

Simplify

3 tan (\frac{x}{4}) = 3

3 tan (\frac{x}{4}) = 3

Divide both sides by

3

3 tan (\frac{x}{4}) = 3

Divide both sides by

3

\frac{3 tan ( \frac{x}{4} )}{3} = \frac{3}{3}

Simplify

tan (\frac{x}{4}) = \frac{3}{3}

tan (\frac{x}{4}) = \frac{3}{3}

General solutions for

tan (\frac{x}{4}) = \frac{3}{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}{4} = \frac{π}{6} + πn

\frac{x}{4} = \frac{π}{6} + πn

Solve

\frac{x}{4} = \frac{π}{6} + πn : x = \frac{2 π}{3} + 4 πn

\frac{x}{4} = \frac{π}{6} + πn

Multiply both sides by

4

\frac{x}{4} = \frac{π}{6} + πn

Multiply both sides by

4

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

Simplify

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

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

4 \cdot \frac{π}{6} + 4 πn : \frac{2 π}{3} + 4 πn

4 \cdot \frac{π}{6} + 4 πn

4 \cdot \frac{π}{6} = \frac{2 π}{3}

4 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 4}{6}

Cancel the common factor:

2

= \frac{2 π}{3}

= \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

sin^{2} (3 x) = 1

2 - - 1 - 6 sin (x) = - 4 sin (x)

2 sin (\frac{x}{2}) - 1 = 0

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

2 tan^{2} (t) = - 3 sec (t)

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