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

The general solution for tan(t)=-1/(sqrt(3)) is t=(5pi)/6+pin

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tan(t)=-1/(sqrt(3))

tan (t) = - \frac{1}{3}

t = \frac{5 π}{6} + πn

Solution steps

tan (t) = - \frac{1}{3}

Simplify

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

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

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

General solutions for

tan (t) = - \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}

t = \frac{5 π}{6} + πn

t = \frac{5 π}{6} + πn

0 = 2 cos (θ) sin (θ) + cos (θ)

sin (x) = \frac{1}{2} tan (x)

8 (1 - cos (θ)) = sin^{2} (θ)

x, cos (x) = sin (x)

cos (2 θ) - cos (θ) = - 1

What is the general solution for tan(t)=-1/(sqrt(3)) ?
The general solution for tan(t)=-1/(sqrt(3)) is t=(5pi)/6+pin