Cotangent of Three Right Angles less Angle
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Theorem
- $\cot \left({\dfrac {3 \pi} 2 - \theta}\right) = \tan \theta$
where $\cot$ and $\tan$ are cotangent and tangent respectively.
Proof
\(\ds \cot \left({\frac {3 \pi} 2 - \theta}\right)\) | \(=\) | \(\ds \frac {\cos \left({\frac {3 \pi} 2 - \theta}\right)} {\sin \left({\frac {3 \pi} 2 - \theta}\right)}\) | Cotangent is Cosine divided by Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {-\sin \theta} {-\cos \theta}\) | Cosine of Three Right Angles and Sine of Three Right Angles | |||||||||||
\(\ds \) | \(=\) | \(\ds \tan \theta\) | Tangent is Sine divided by Cosine |
$\blacksquare$
Also see
- Sine of Three Right Angles less Angle
- Cosine of Three Right Angles less Angle
- Tangent of Three Right Angles less Angle
- Secant of Three Right Angles less Angle
- Cosecant of Three Right Angles less 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