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

2 sin (2 x) = tan (2 x)

sin^{2} (3 a) = 0.56

cos (x) = 0.22

3 cos (b) - 1 = 5 cos (b) + 1

sin (- x) = cos (x)

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