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
Start Watching
Lessons
  1. Tangents of Polar Curves Overview
?
Examples
Start Watching
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
      Free to Join!
      StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.

      • Easily See Your Progress

        We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.

      • Make Use of Our Learning Aids

        Last Viewed
        Practice Accuracy
        Suggested Tasks

        Get quick access to the topic you're currently learning.

        See how well your practice sessions are going over time.

        Stay on track with our daily recommendations.

      • Earn Achievements as You Learn

        Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.

      • Create and Customize Your Avatar

        Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
      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
      ?