"How do you evaluate tan⁡(π6)?" solved and explained

High School
Geometry
Trigonometry
Trigonometric Functions

Pamela Meyer

Answered question

2021-12-31

How do you evaluate

\tan (\frac{π}{6})

Answer & Explanation

Thomas Lynn

Beginner2022-01-01Added 28 answers

Explanation:

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

hope that helped

karton

Expert2022-01-08Added 613 answers

Using the identity
$\tan = \frac{\sin}{\cos}$
and
$\sin (\frac{π}{6}) = \sin (30) = \frac{1}{2}$
$\cos (\frac{π}{6}) = \cos (30) = \frac{\sqrt{3}}{2}$
then
$\tan (\frac{π}{6}) = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$
You should know that dividing by one number is the same as multiplying by its reciprocal, so
$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{2} \cdot \frac{2}{\sqrt{3}}$
Cancelling the 2's and rationalising the denominator,
$\frac{1}{2} \cdot \frac{2}{\sqrt{3}} = \frac{1}{\sqrt{3}}$
$\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}$
Therefore,
$\tan (\frac{π}{6}) = \frac{\sqrt{3}}{3}$
Using a calculator.
$\tan (\frac{π}{6}) =\approx 0.577$

user_27qwe

Skilled2022-01-08Added 375 answers

Thank u a lot

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