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

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

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tan(a)= 1/(sqrt(3))

tan (a) = \frac{1}{3}

a = \frac{π}{6} + πn

Solution steps

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

General solutions for

tan (a) = \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}

a = \frac{π}{6} + πn

a = \frac{π}{6} + πn

tan (x) = 0.649

\frac{sin ( x ) + cos ( x )}{cos ( x ) + 1} = tan (x)

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

tan (θ) = \frac{1}{2}

- cos (x) - sin (x) = 1

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