What is the general solution for 3cot(1/4 x)=sqrt(3) ?

The general solution for 3cot(1/4 x)=sqrt(3) is x=(4pi)/3+4pin

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3cot(1/4 x)=sqrt(3)

3 cot (\frac{1}{4} x) = 3

x = \frac{4 π}{3} + 4 πn

Degrees

x = 24 0^{\circ} + 72 0^{\circ} n

Solution steps

3 cot (\frac{1}{4} x) = 3

Divide both sides by

3

3 cot (\frac{1}{4} x) = 3

Divide both sides by

3

\frac{3 cot ( \frac{1}{4} x )}{3} = \frac{3}{3}

Simplify

cot (\frac{1}{4} x) = \frac{3}{3}

cot (\frac{1}{4} x) = \frac{3}{3}

General solutions for

cot (\frac{1}{4} x) = \frac{3}{3}

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

\frac{1}{4} x = \frac{π}{3} + πn

\frac{1}{4} x = \frac{π}{3} + πn

Solve

\frac{1}{4} x = \frac{π}{3} + πn : x = \frac{4 π}{3} + 4 πn

\frac{1}{4} x = \frac{π}{3} + πn

Multiply both sides by

4

\frac{1}{4} x = \frac{π}{3} + πn

Multiply both sides by

4

4 \cdot \frac{1}{4} x = 4 \cdot \frac{π}{3} + 4 πn

Simplify

4 \cdot \frac{1}{4} x = 4 \cdot \frac{π}{3} + 4 πn

Simplify

4 \cdot \frac{1}{4} x : x

4 \cdot \frac{1}{4} x

Multiply fractions:

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

= \frac{1 \cdot 4}{4} x

Cancel the common factor:

4

= x \cdot 1

Multiply:

x \cdot 1 = x

= x

Simplify

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

4 \cdot \frac{π}{3} + 4 πn

Multiply

4 \cdot \frac{π}{3} : \frac{4 π}{3}

4 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 4}{3}

= \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

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

2 sin^{2} (t) - 3 sin (t) + 1 = 0

5 sin (x) = 0

5 sin (x) = 4

5 sin (x) = 3

What is the general solution for 3cot(1/4 x)=sqrt(3) ?
The general solution for 3cot(1/4 x)=sqrt(3) is x=(4pi)/3+4pin