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