Pamela Meyer

## Answered question

2021-12-31

How do you evaluate $\mathrm{tan}\left(\frac{\pi }{6}\right)$?

### Answer & Explanation

Thomas Lynn

Beginner2022-01-01Added 28 answers

Explanation:
$\mathrm{tan}\left(\frac{\pi }{6}\right)=\frac{\mathrm{sin}\left(\frac{\pi }{6}\right)}{\mathrm{cos}\left(\frac{\pi }{6}\right)}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$
hope that helped

karton

Expert2022-01-08Added 613 answers

Using the identity
$\mathrm{tan}=\frac{\mathrm{sin}}{\mathrm{cos}}$
and
$\mathrm{sin}\left(\frac{\pi }{6}\right)=\mathrm{sin}\left(30\right)=\frac{1}{2}$
$\mathrm{cos}\left(\frac{\pi }{6}\right)=\mathrm{cos}\left(30\right)=\frac{\sqrt{3}}{2}$
then
$\mathrm{tan}\left(\frac{\pi }{6}\right)=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$
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,
$\mathrm{tan}\left(\frac{\pi }{6}\right)=\frac{\sqrt{3}}{3}$
Using a calculator.
$\mathrm{tan}\left(\frac{\pi }{6}\right)=\approx 0.577$

user_27qwe

Skilled2022-01-08Added 375 answers

Thank u a lot

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?