What is the general solution for tan(α)=(12)/(6sqrt(3)) ?

The general solution for tan(α)=(12)/(6sqrt(3)) is α=0.85707…+pin

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tan(α)=(12)/(6sqrt(3))

tan (α) = \frac{12}{6 3}

α = 0.85707 \dots + πn

Solution steps

tan (α) = \frac{12}{6 3}

Simplify

\frac{12}{6 3} : \frac{2 3}{3}

\frac{12}{6 3}

Divide the numbers:

\frac{12}{6} = 2

= \frac{2}{3}

Rationalize

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

= \frac{2 3}{3}

tan (α) = \frac{2 3}{3}

Apply trig inverse properties

tan (α) = \frac{2 3}{3}

General solutions for

tan (α) = \frac{2 3}{3}

tan (x) = a \Rightarrow x = arctan (a) + πn

α = arctan (\frac{2 3}{3}) + πn

α = arctan (\frac{2 3}{3}) + πn

Show solutions in decimal form

α = 0.85707 \dots + πn

1 = cos^{2} (α) - 2 cos (α) sin (a) + sin^{2} (α)

4 sin (θ) = 1

sin (x + \frac{π}{2}) = 0.6

4 cot (x) + 1 = 1 + 2 cot (x)

\frac{2}{3} = sin (θ) - 0.28 cos (θ)

What is the general solution for tan(α)=(12)/(6sqrt(3)) ?
The general solution for tan(α)=(12)/(6sqrt(3)) is α=0.85707…+pin