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

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

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tan(θ)=(-2sqrt(3))/2

tan (θ) = \frac{- 2 3}{2}

θ = \frac{2 π}{3} + πn

Solution steps

tan (θ) = \frac{- 2 3}{2}

Simplify

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

\frac{- 2 3}{2}

Apply the fraction rule:

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

= - \frac{2 3}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 3

General solutions for

tan (θ) = - 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{2 π}{3} + πn

θ = \frac{2 π}{3} + πn

sec (4 x) - 9 = 0

\frac{1}{3} cos (θ) = - \frac{3}{6}

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

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

3 sin (2 x - 1 5^{\circ}) = cos (2 x - 1 5^{\circ})

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