What is the general solution for tan(θ)=(sqrt(3))/(-1) ?

The general solution for tan(θ)=(sqrt(3))/(-1) is θ=(2pi)/3+pin

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tan(θ)=(sqrt(3))/(-1)

tan (θ) = \frac{3}{- 1}

θ = \frac{2 π}{3} + πn

Solution steps

tan (θ) = \frac{3}{- 1}

Simplify

\frac{3}{- 1} : - 3

\frac{3}{- 1}

Apply the fraction rule:

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

= - \frac{3}{1}

Apply rule

\frac{a}{1} = a

= - 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

cos (x) = \frac{8}{10}

2 sin^{2} (x) + 3 = 0

cos (x) + \frac{1}{2} = 0

cot (\frac{2 x}{3}) = - 3

sin (x) - 2 sin^{2} (x) = 0

What is the general solution for tan(θ)=(sqrt(3))/(-1) ?
The general solution for tan(θ)=(sqrt(3))/(-1) is θ=(2pi)/3+pin