What is the general solution for tan(x/3)=1,0<= x<= 2pi ?

The general solution for tan(x/3)=1,0<= x<= 2pi is x=(3pi)/4

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tan(x/3)=1,0<= x<= 2pi

tan (\frac{x}{3}) = 1, 0 \leq x \leq 2 π

x = \frac{3 π}{4}

Degrees

x = 13 5^{\circ}

Solution steps

tan (\frac{x}{3}) = 1, 0 \leq x \leq 2 π

General solutions for

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

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}{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

Solutions for the range

0 \leq x \leq 2 π

x = \frac{3 π}{4}

4 sin (x) = sin (x) tan (x)

cos (x) = 0.707

4 cos^{2} (x) - 4 cos (x) - 3 = 0

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

tan (θ) = - \frac{5}{2}

What is the general solution for tan(x/3)=1,0<= x<= 2pi ?
The general solution for tan(x/3)=1,0<= x<= 2pi is x=(3pi)/4