"Find the exact value of π6" was answered by our community

Nicontio1

Answered question

2021-12-13

Find the exact value of

\frac{π}{6}

jgardner33v4

Beginner2021-12-14Added 35 answers

\tan = \frac{\sin}{\cos}

\sin (\frac{π}{6}) = \sin (30) = \frac{1}{2}

\cos (\frac{π}{6}) = \cos (30) = \frac{\sqrt{3}}{2}

Then

\tan (\frac{π}{6}) = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}

\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{2} \times \frac{2}{\sqrt{3}}

Rationalise the denominator

\frac{1}{2} \times \frac{2}{\sqrt{3}} = \frac{1}{\sqrt{3}}

\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}

Therefore,

\tan (\frac{π}{6}) = \frac{\sqrt{3}}{3}

Laura Worden

Beginner2021-12-15Added 45 answers

\frac{π}{6} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}

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