5.6.2: Key Equations

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May 28, 2023
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- 5.6.1: Key Terms
- 5.6.3: Key Concepts

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Key Equations

arc length	$s = r θ$
area of a sector	$A = \frac{1}{2} θ r^{2}$
angular speed	$ω = \frac{θ}{t}$
linear speed	$v = \frac{s}{t}$
linear speed related to angular speed	$v = r ω$

Cosine	$\cos t = x$
Sine	$\sin t = y$
Pythagorean Identity	$\cos^{2} t + \sin^{2} t = 1$

Tangent function	$\tan t = \frac{\sin t}{\cos t}$
Secant function	$\sec t = \frac{1}{\cos t}$
Cosecant function	$\csc t = \frac{1}{\sin t}$
Cotangent function	$\cot t = \frac{1}{\tan t} = \frac{\cos t}{\sin t}$

Cofunction Identities

$\begin{array}{l} \begin{array}{l} \cos t = \sin (\frac{π}{2} - t) \end{array} \\ \sin t = \cos (\frac{π}{2} - t) \\ \tan t = \cot (\frac{π}{2} - t) \\ \cot t = \tan (\frac{π}{2} - t) \\ \sec t = \csc (\frac{π}{2} - t) \\ \csc t = \sec (\frac{π}{2} - t) \end{array}$

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