# Tangent of 225 Degrees

From ProofWiki

## Theorem

- $\tan 225^\circ = \tan \dfrac {5 \pi} 4 = 1$

where $\tan$ denotes tangent.

## Proof

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \tan 225^\circ\) | \(=\) | \(\displaystyle \) | \(\) | \(\displaystyle \) | \(\displaystyle \tan \left({360^\circ - 135^\circ}\right)\) | \(\displaystyle \) | \(\displaystyle \) | |||

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(=\) | \(\displaystyle \) | \(\) | \(\displaystyle \) | \(\displaystyle -\tan 135^\circ\) | \(\displaystyle \) | \(\displaystyle \) | Tangent of Conjugate Angle | ||

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(=\) | \(\displaystyle \) | \(\) | \(\displaystyle \) | \(\displaystyle 1\) | \(\displaystyle \) | \(\displaystyle \) | Tangent of 135 Degrees |

$\blacksquare$

## Sources

- Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*(1968)... (previous)... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles