Tangent of Angle plus Right Angle
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Theorem
- $\map \tan {x + \dfrac \pi 2} = -\cot x$
Proof
\(\ds \map \tan {x + \frac \pi 2}\) | \(=\) | \(\ds \frac {\map \sin {x + \frac \pi 2} } {\map \cos {x + \frac \pi 2} }\) | Tangent is Sine divided by Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\cos x} {- \sin x}\) | Sine of Angle plus Right Angle and Cosine of Angle plus Right Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds -\cot x\) | Cotangent is Cosine divided by Sine |
$\blacksquare$
Also see
- Sine of Angle plus Right Angle
- Cosine of Angle plus Right Angle
- Cotangent of Angle plus Right Angle
- Secant of Angle plus Right Angle
- Cosecant of Angle plus Right Angle
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercise $\text {XXXI}$: $6.$
- 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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $12$: Trigonometric formulae: Shifts and periodicity
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $14$: Trigonometric formulae: Shifts and periodicity