Tangents of polar curves  Parametric Equations and Polar Coordinates
Tangents of polar curves
In this lesson, we will learn how to find the tangent line of polar curves. Just like how we can find the tangent of Cartesian and parametric equations, we can do the same for polar equations. First, we will examine a generalized formula to taking the derivative, and apply it to finding tangents. Then we will look at a few examples to finding the first derivative. Lastly, we will do some applications which involve finding tangent lines of polar curves at a specified point.
Basic concepts:
 Power rule
 Derivative of trigonometric functions
 Derivative of exponential functions
 Polar coordinates
Related concepts:
 Slope and equation of tangent line
Lessons
Notes:
In order to find the tangent line to polar curves, we have to take the derivative in polar coordinates.
Here is the formula to take the derivative in polar coordinates:
$\frac{dy}{dx}=\frac{\frac{dr}{d \theta}\sin \theta+r\;\cos \theta}{\frac{dr}{d \theta}\cos \thetar\;\sin \theta}$

1.
Finding the Derivative
Find $\frac{dy}{dx}$ for each of the following polar equations: