Pamela Meyer

2021-12-31

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

Thomas Lynn

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

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