Tangent of 30 Degrees

From ProofWiki
Jump to navigation Jump to search

Theorem

$\tan 30 \degrees = \tan \dfrac \pi 6 = \dfrac {\sqrt 3} 3$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 30 \degrees\) \(=\) \(\ds \frac {\sin 30 \degrees} {\cos 30 \degrees}\) Tangent is Sine divided by Cosine
\(\ds \) \(=\) \(\ds \frac {\frac 1 2} {\frac {\sqrt 3} 2}\) Sine of $30 \degrees$ and Cosine of $30 \degrees$
\(\ds \) \(=\) \(\ds \frac 1 {\sqrt 3}\)
\(\ds \) \(=\) \(\ds \frac {\sqrt 3} 3\) multiplying top and bottom by $\sqrt 3$

$\blacksquare$


Also presented as

Some sources present the tangent of $30 \degrees$ as:

$\tan 30 \degrees = \tan \dfrac \pi 6 = \dfrac 1 {\sqrt 3}$


Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Tangent_of_30_Degrees&oldid=725044"