What is the general solution for sqrt(3)=tan(θ/3) ?

The general solution for sqrt(3)=tan(θ/3) is θ=pi+3pin

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sqrt(3)=tan(θ/3)

3 = tan (\frac{θ}{3})

θ = π + 3 πn

Degrees

θ = 18 0^{\circ} + 54 0^{\circ} n

Solution steps

3 = tan (\frac{θ}{3})

Switch sides

tan (\frac{θ}{3}) = 3

General solutions for

tan (\frac{θ}{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{θ}{3} = \frac{π}{3} + πn

\frac{θ}{3} = \frac{π}{3} + πn

Solve

\frac{θ}{3} = \frac{π}{3} + πn : θ = π + 3 πn

\frac{θ}{3} = \frac{π}{3} + πn

Multiply both sides by

3

\frac{θ}{3} = \frac{π}{3} + πn

Multiply both sides by

3

\frac{3 θ}{3} = 3 \cdot \frac{π}{3} + 3 πn

Simplify

\frac{3 θ}{3} = 3 \cdot \frac{π}{3} + 3 πn

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

3 \cdot \frac{π}{3} + 3 πn : π + 3 πn

3 \cdot \frac{π}{3} + 3 πn

3 \cdot \frac{π}{3} = π

3 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 3}{3}

Cancel the common factor:

3

= π

= π + 3 πn

θ = π + 3 πn

θ = π + 3 πn

θ = π + 3 πn

θ = π + 3 πn

sec (x) - 2 = 0, 0 \leq x < 2 π

cos (x) = \frac{15}{19}

cos^{3} (x) = - \frac{1}{2}

(sec (x) + 1)^{2} - tan (x) = 0

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

What is the general solution for sqrt(3)=tan(θ/3) ?
The general solution for sqrt(3)=tan(θ/3) is θ=pi+3pin