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

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

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1=tan(x/3)

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

x = \frac{3 π}{4} + 3 πn

Degrees

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

Solution steps

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

Switch sides

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

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

cos (12 x) = 0

cos (2 x + 1) = \frac{1}{2}

2 ∣ sin (4 x) ∣ = 0

sin (α) = - \frac{3}{5}

sin (2 x) = \frac{2 \cdot ( 1 \cdot 1 0 ^{12} )}{( 1 \cdot 1 0 ^{7} ) ^{2}}

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