What is the general solution for tan(θ)-1/(sqrt(3))=0 ?

The general solution for tan(θ)-1/(sqrt(3))=0 is θ= pi/6+pin

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tan(θ)-1/(sqrt(3))=0

tan (θ) - \frac{1}{3} = 0

θ = \frac{π}{6} + πn

Degrees

θ = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

tan (θ) - \frac{1}{3} = 0

Move

\frac{1}{3}

to the right side

tan (θ) - \frac{1}{3} = 0

Add

\frac{1}{3}

to both sides

tan (θ) - \frac{1}{3} + \frac{1}{3} = 0 + \frac{1}{3}

Simplify

tan (θ) - \frac{1}{3} + \frac{1}{3} = 0 + \frac{1}{3}

Simplify

tan (θ) - \frac{1}{3} + \frac{1}{3} : tan (θ)

tan (θ) - \frac{1}{3} + \frac{1}{3}

Add similar elements:

- \frac{1}{3} + \frac{1}{3} = 0

= tan (θ)

Simplify

0 + \frac{1}{3} : \frac{3}{3}

0 + \frac{1}{3}

0 + \frac{1}{3} = \frac{1}{3}

= \frac{1}{3}

Rationalize

\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}

= \frac{3}{3}

tan (θ) = \frac{3}{3}

tan (θ) = \frac{3}{3}

tan (θ) = \frac{3}{3}

General solutions for

tan (θ) = \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}

θ = \frac{π}{6} + πn

θ = \frac{π}{6} + πn

tan (\frac{x}{2} + \frac{π}{3}) = 1

- cot (x) + csc (x) = 1

cot (\frac{x}{2}) = 0

sin^{2} (θ) = 2 sin (θ) + 3

sin (3 x) + sin (5 x) = 0

What is the general solution for tan(θ)-1/(sqrt(3))=0 ?
The general solution for tan(θ)-1/(sqrt(3))=0 is θ= pi/6+pin