interdicoxd

2021-12-31

Find the value of $\mathrm{tan}\left(\frac{\pi }{3}\right)$

Neil Dismukes

Expert

Well, $\mathrm{tan}\left(\frac{\pi }{3}\right)=\frac{\mathrm{sin}\left(\frac{\pi }{3}\right)}{\mathrm{cos}\left(\frac{\pi }{3}\right)}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\sqrt{3}}{2}\left(\frac{2}{1}\right)=\sqrt{3}$
However, you can find it in another way:
Just think of it as a $\mathrm{tan}60°$ and then draw a $30°-60°-90°$ tringle
And $\mathrm{tan}60°$ will be equal to $\frac{opposite}{adjacent}$ in reference to $60°$ angle. Thus, $opposite=\sqrt{3}$ and $adjacent=1$. Hence,
$\mathrm{tan}60°=\frac{opposite}{adjacent}=\frac{\sqrt{3}}{1}=\sqrt{3}$

twineg4

Expert

Use the Unit Circle and examine it at $\frac{\pi }{3}$
And determine the tangent, if we know the point $\left(\left\{\frac{\sqrt{3}}{2};\left\{\frac{1}{2}\right)$, thinking of it as a slope of the line in the unit circle.
$\mathrm{tan}\frac{\pi }{3}=\frac{\frac{\sqrt{3}}{2}-0}{\frac{1}{2}-0}=\sqrt{3}$

nick1337

Expert

$\mathrm{tan}\left(\frac{\pi }{3}\right)=\sqrt{3}$