Tangent of 225 Degrees
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Theorem
- $\tan 225 \degrees = \tan \dfrac {5 \pi} 4 = 1$
where $\tan$ denotes tangent.
Proof
| \(\ds \tan 225 \degrees\) | \(=\) | \(\ds \map \tan {360 \degrees - 135 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\tan 135 \degrees\) | Tangent of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1\) | Tangent of $135 \degrees$ |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles