5.6.2: Key Equations

Key Equations

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

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

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