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

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

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tan(x)=(-sqrt(3))/3

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

x = \frac{5 π}{6} + πn

Degrees

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

Solution steps

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

Apply the fraction rule:

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

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

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

12 sin^{2} (x) + sin (x) - 1 = 0

2 sin^{2} (2 x) - 1 = 0

- 5 (sec (x) - 2) (2 sin (x) + 3) = 0

5 sec^{2} (x) - 5 = 0

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