What is the general solution for -4sqrt(3)=12tan(θ) ?

The general solution for -4sqrt(3)=12tan(θ) is θ=(5pi)/6+pin

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-4sqrt(3)=12tan(θ)

- 43 = 12 tan (θ)

θ = \frac{5 π}{6} + πn

Degrees

θ = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

- 43 = 12 tan (θ)

Switch sides

12 tan (θ) = - 43

Divide both sides by

12

12 tan (θ) = - 43

Divide both sides by

12

\frac{12 tan ( θ )}{12} = \frac{- 4 3}{12}

Simplify

\frac{12 tan ( θ )}{12} = \frac{- 4 3}{12}

Simplify

\frac{12 tan ( θ )}{12} : tan (θ)

\frac{12 tan ( θ )}{12}

Divide the numbers:

\frac{12}{12} = 1

= tan (θ)

Simplify

\frac{- 4 3}{12} : - \frac{3}{3}

\frac{- 4 3}{12}

Apply the fraction rule:

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

= - \frac{4 3}{12}

Cancel the common factor:

4

= - \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

tan (2 θ) = 2.4

3 sin^{2} (θ) = 2 sin (θ) + 3

\frac{sin ( 18 0 ^{\circ} )}{20} = \frac{sin ( a )}{8}

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

tan (4 x) = 12

What is the general solution for -4sqrt(3)=12tan(θ) ?
The general solution for -4sqrt(3)=12tan(θ) is θ=(5pi)/6+pin