What is the general solution for 2sqrt(3)=-6tan(θ) ?

The general solution for 2sqrt(3)=-6tan(θ) is θ=(5pi)/6+pin

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2sqrt(3)=-6tan(θ)

23 = - 6 tan (θ)

θ = \frac{5 π}{6} + πn

Degrees

θ = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

23 = - 6 tan (θ)

Switch sides

- 6 tan (θ) = 23

Divide both sides by

- 6

- 6 tan (θ) = 23

Divide both sides by

- 6

\frac{- 6 tan ( θ )}{- 6} = \frac{2 3}{- 6}

Simplify

\frac{- 6 tan ( θ )}{- 6} = \frac{2 3}{- 6}

Simplify

\frac{- 6 tan ( θ )}{- 6} : tan (θ)

\frac{- 6 tan ( θ )}{- 6}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{6 tan ( θ )}{6}

Divide the numbers:

\frac{6}{6} = 1

= tan (θ)

Simplify

\frac{2 3}{- 6} : - \frac{3}{3}

\frac{2 3}{- 6}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 3}{6}

Cancel the common factor:

2

= - \frac{3}{3}

tan (θ) = - \frac{3}{3}

tan (θ) = - \frac{3}{3}

tan (θ) = - \frac{3}{3}

General solutions for

tan (θ) = - \frac{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}

θ = \frac{5 π}{6} + πn

θ = \frac{5 π}{6} + πn

What is the general solution for 2sqrt(3)=-6tan(θ) ?
The general solution for 2sqrt(3)=-6tan(θ) is θ=(5pi)/6+pin