How do you find the slope of the line tangent to the polar graph of r = f(θ) at a point?
Consider the following polar equation ;
r = f(
The objective is to find the slope of the line tangent to the given polar graph.
We know that the polar point in cartesian coordinates is x = rcos( , y = r sin(
The given polar equation is r = f(
Therefore , the cartesian coordinates are given as ;
x= f( , y = f(sin(.
Hence , the parametric form in cartesian coordinates are ; x= f( , y = f(sin(.
We , know that the slope of the line tangent is ;
So, describing x and y in terms of ‘ alone.So , using the chain rule we compute
Since , = .
Now , we will need the following derivatives.
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
Since the solution to 2E from 10.3 chapter was answered, more than 259 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Find, graph, line, point, polar. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 2E from chapter: 10.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “How do you find the slope of the line tangent to the polar graph of r = f(?) at a point?” is broken down into a number of easy to follow steps, and 21 words.