Cosine of Three Right Angles
Theorem
- $\cos 270 \degrees = \cos \dfrac {3 \pi} 2 = 0$
where $\cos$ denotes cosine.
Proof
| \(\ds \cos 270 \degrees\) | \(=\) | \(\ds \map \cos {360 \degrees - 90 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \cos 90 \degrees\) | Cosine of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds 0\) | Cosine of Right Angle |
$\blacksquare$
Also see
- Sine of Three Right Angles
- Tangent of Three Right Angles
- Cotangent of Three Right Angles
- Secant of Three Right Angles
- Cosecant of Three Right Angles
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Special angles
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles