What is the general solution for 3tan(x)=-sqrt(3) ?

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

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3tan(x)=-sqrt(3)

3 tan (x) = - 3

x = \frac{5 π}{6} + πn

Degrees

x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

3 tan (x) = - 3

Divide both sides by

3

3 tan (x) = - 3

Divide both sides by

3

\frac{3 tan ( x )}{3} = \frac{- 3}{3}

Simplify

tan (x) = - \frac{3}{3}

tan (x) = - \frac{3}{3}

General solutions for

tan (x) = - \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}

x = \frac{5 π}{6} + πn

x = \frac{5 π}{6} + πn

5 sin (x) + 2 = sin (x)

tan^{2} (θ) + tan (θ) = 0

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

cos (2 x) = cos (x) - 1

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

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