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	$v=r\omega$

Trigonometric Functions	$\begin{array}{cc}\text{Sine}\hfill & \text{sin }t=\frac{\text{opposite}}{\text{hypotenuse}}\hfill \\ \text{Cosine}\hfill & \text{cos }t=\frac{\text{adjacent}}{\text{hypotenuse}}\hfill \\ \text{Tangent}\hfill & \text{tan }t=\frac{\text{opposite}}{\text{adjacent}}\hfill \\ \text{Secant}\hfill & \text{sec }t=\frac{\text{hypotenuse}}{\text{adjacent}}\hfill \\ \text{Cosecant}\hfill & \text{csc }t=\frac{\text{hypotenuse}}{\text{opposite}}\hfill \\ \text{Cotangent}\hfill & \text{cot }t=\frac{\text{adjacent}}{\text{opposite}}\hfill \end{array}$
Reciprocal Trigonometric Functions	$\begin{array}{cc}\text{sin }t=\frac{1}{\text{csc }t}\hfill & \text{csc }t=\frac{1}{\text{sin }t}\hfill \\ \text{cos }t=\frac{1}{\text{sec }t}\hfill & \text{sec }t=\frac{1}{\text{cos }t}\hfill \\ \text{tan }t=\frac{1}{\text{cot }t}\hfill & \text{cot }t=\frac{1}{\text{tan }t}\hfill \end{array}$
Cofunction Identities	$\begin{array}{c}\text{cos }t=\sin \left(\frac{\pi }{2}-t\right)\hfill \\ \text{sin }t=\cos \left(\frac{\pi }{2}-t\right)\hfill \\ \text{tan }t=\cot \left(\frac{\pi }{2}-t\right)\hfill \\ \text{cot }t=\tan \left(\frac{\pi }{2}-t\right)\hfill \\ \text{sec }t=\csc \left(\frac{\pi }{2}-t\right)\hfill \end{array}$

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	$\text{cot}t=\frac{1}{\text{tan}t}=\frac{\text{cos}t}{\text{sin}t}$