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

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

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6tan(θ)=-2sqrt(3)

6 tan (θ) = - 23

θ = \frac{5 π}{6} + πn

Degrees

θ = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

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}

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

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

sin (x) + 1 = 2 1 - sin^{2} (x)

cot (θ) = 0.6

sin^{2} (2 x) + 3 sin (2 x) + 2 = 0, 0 \leq x \leq 10 π

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

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