What is the general solution for 3sqrt(3)tan(u)=3 ?

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

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3sqrt(3)tan(u)=3

33 tan (u) = 3

u = \frac{π}{6} + πn

Degrees

u = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

33 tan (u) = 3

Divide both sides by

33

33 tan (u) = 3

Divide both sides by

33

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

Simplify

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

Simplify

\frac{3 3 tan ( u )}{3 3} : tan (u)

\frac{3 3 tan ( u )}{3 3}

Divide the numbers:

\frac{3}{3} = 1

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

Cancel the common factor:

3

= tan (u)

Simplify

\frac{3}{3 3} : \frac{3}{3}

\frac{3}{3 3}

Divide the numbers:

\frac{3}{3} = 1

= \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 (u) = \frac{3}{3}

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

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

General solutions for

tan (u) = \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}

u = \frac{π}{6} + πn

u = \frac{π}{6} + πn

3 sec (2 x + 3) = 4

t, f = 3 cos (ptt h e t a) - 2

sin (θ - π) = - \frac{1}{2}

7 - 2 sin (5 (x + \frac{π}{8})) = 9

x, 4 cos^{2} (x) = 3

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