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

The general solution for sqrt(3)-tan(3θ)=0 is θ= pi/9+(pin)/3

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sqrt(3)-tan(3θ)=0

3 - tan (3 θ) = 0

θ = \frac{π}{9} + \frac{πn}{3}

Degrees

θ = 2 0^{\circ} + 6 0^{\circ} n

Solution steps

3 - tan (3 θ) = 0

Move

3

to the right side

3 - tan (3 θ) = 0

Subtract

3

from both sides

3 - tan (3 θ) - 3 = 0 - 3

Simplify

- tan (3 θ) = - 3

- tan (3 θ) = - 3

Divide both sides by

- 1

- tan (3 θ) = - 3

Divide both sides by

- 1

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

Simplify

tan (3 θ) = 3

tan (3 θ) = 3

General solutions for

tan (3 θ) = 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}

3 θ = \frac{π}{3} + πn

3 θ = \frac{π}{3} + πn

Solve

3 θ = \frac{π}{3} + πn : θ = \frac{π}{9} + \frac{πn}{3}

3 θ = \frac{π}{3} + πn

Divide both sides by

3

3 θ = \frac{π}{3} + πn

Divide both sides by

3

\frac{3 θ}{3} = \frac{\frac{π}{3}}{3} + \frac{πn}{3}

Simplify

\frac{3 θ}{3} = \frac{\frac{π}{3}}{3} + \frac{πn}{3}

Simplify

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

Divide the numbers:

\frac{3}{3} = 1

= θ

Simplify

\frac{\frac{π}{3}}{3} + \frac{πn}{3} : \frac{π}{9} + \frac{πn}{3}

\frac{\frac{π}{3}}{3} + \frac{πn}{3}

\frac{\frac{π}{3}}{3} = \frac{π}{9}

\frac{\frac{π}{3}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{π}{9}

= \frac{π}{9} + \frac{πn}{3}

θ = \frac{π}{9} + \frac{πn}{3}

θ = \frac{π}{9} + \frac{πn}{3}

θ = \frac{π}{9} + \frac{πn}{3}

θ = \frac{π}{9} + \frac{πn}{3}

3 cot (3 x) - 3 = 0

3 + sin (y) = 3 cos^{2} (y)

cos (α) = \frac{3}{2}

tan (t) = - \frac{4}{3}

sin^{2} (x) = 0.25

What is the general solution for sqrt(3)-tan(3θ)=0 ?
The general solution for sqrt(3)-tan(3θ)=0 is θ= pi/9+(pin)/3