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

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

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cot(x/3)=1

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

x = \frac{3 π}{4} + 3 πn

Degrees

x = 13 5^{\circ} + 54 0^{\circ} n

Solution steps

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

General solutions for

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

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{x}{3} = \frac{π}{4} + πn

\frac{x}{3} = \frac{π}{4} + πn

Solve

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

\frac{x}{3} = \frac{π}{4} + πn

Multiply both sides by

3

\frac{x}{3} = \frac{π}{4} + πn

Multiply both sides by

3

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

Simplify

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

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

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

3 \cdot \frac{π}{4} + 3 πn

Multiply

3 \cdot \frac{π}{4} : \frac{3 π}{4}

3 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 3}{4}

= \frac{3 π}{4} + 3 πn

x = \frac{3 π}{4} + 3 πn

x = \frac{3 π}{4} + 3 πn

x = \frac{3 π}{4} + 3 πn

x = \frac{3 π}{4} + 3 πn

tan (t) = 7

cos (x) + cos (x) = 0

3 cos (x) = 2 + 2 sin (x)

cos (t) = \frac{8}{17}

sin^{2} (x) - 5 sin (x) cos (x) + 6 cos^{2} (x) = 0

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