Cotangent of Angle plus Right Angle
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Theorem
- $\map \cot {x + \dfrac \pi 2} = -\tan x$
Proof
\(\ds \map \cot {x + \frac \pi 2}\) | \(=\) | \(\ds \frac {\map \cos {x + \frac \pi 2} } {\map \sin {x + \frac \pi 2} }\) | Cotangent is Cosine divided by Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {- \sin x} {\cos x}\) | Cosine of Angle plus Right Angle and Sine of Angle plus Right Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds -\tan x\) | Tangent is Sine divided by Cosine |
$\blacksquare$
Also see
- Sine of Angle plus Right Angle
- Cosine of Angle plus Right Angle
- Tangent of Angle plus Right Angle
- Secant of Angle plus Right Angle
- Cosecant of Angle plus Right Angle
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