Tangents of polar curves

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. Tangents of Polar Curves Overview
?
Examples
Lessons
  1. Finding the Derivative
    Find dydx\frac{dy}{dx} for each of the following polar equations:
    1. r=sin⁡θ+θr=\sin \theta + \theta
    2. r=sin⁡θcos⁡θ r= \frac{\sin \theta}{\cos \theta}
  2. Finding the Tangent Line
    Find the tangent line with the following polar curves at the specified point:
    r=sin⁡(3θ)r=\sin (3\theta) at θ=π4\theta = \frac{\pi}{4}
    1. Finding the Tangent Line
      Find the tangent line with the following polar curves at the specified point:
      r=θcos⁡θ r=\theta \cos \theta at θ=0\theta =0
      Topic Notes
      ?
      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.
      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:
      dydx=drdθsin⁡θ+r  cos⁡θdrdθcos⁡θ−r  sin⁡θ\frac{dy}{dx}=\frac{\frac{dr}{d \theta}\sin \theta+r\;\cos \theta}{\frac{dr}{d \theta}\cos \theta-r\;\sin \theta}
      Basic Concepts
      ?
      Related Concepts
      ?