Cosine of Angle plus Three Right Angles
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Theorem
- $\map \cos {x + \dfrac {3 \pi} 2} = \sin x$
Proof
\(\ds \map \cos {x + \frac {3 \pi} 2}\) | \(=\) | \(\ds \cos x \cos \frac {3 \pi} 2 - \sin x \sin \frac {3 \pi} 2\) | Cosine of Sum | |||||||||||
\(\ds \) | \(=\) | \(\ds \cos x \cdot 0 - \sin x \cdot \paren {-1}\) | Cosine of Three Right Angles and Sine of Three Right Angles | |||||||||||
\(\ds \) | \(=\) | \(\ds \sin x\) |
$\blacksquare$
Also see
- Sine of Angle plus Three Right Angles
- Tangent of Angle plus Three Right Angles
- Cotangent of Angle plus Three Right Angles
- Secant of Angle plus Three Right Angles
- Cosecant of Angle plus Three Right Angles
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I