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posted by  The Jacket on 11/2/2009 3:55:54 PM  |  status: Closed  |  Earned Karma: 50

Polar Coordinates

Course Textbook Chapter Problem Needs by
Calculus Single Variable Calculus (6th) by Stewart 10.3 66 11/3/2009 at 11:00:00 PM
Question Details:
The question asks:
Use the given equation to answer the following questions.
r = e^θ
0 ≤ θ < 2π

(a) Find the points on the given curve where the tangent line is horizontal.
θ =    (smaller value)
θ =    (larger value)

(b) Find the points on the given curve where the tangent line is vertical.
θ =  (smaller value)
θ = (larger value)

When I work out the problems, I get -pi/4, but am confused really how to go about solving this. Will rate lifesaver.
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Oracle
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(Drexel University)
posted by The Big Unit on 11/2/2009 4:33:24 PM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
Here is a helpful picture of the polar curve  on :
A horizontal tangent line will occur where  and . A vertical tangent line will occur when  and .
Obtaining the parametric representation of the above logarithmic spiral yields:
So  if . So you will have horizontal tangent lines at  
Also,  if . So you will have vertical tangent lines at
Please feel free to message me with any questions you may have about the problem.
Jon AKA THE BIG UNIT
If you have any questions about the problem, just message me and I will help you out. Hope this helps!
 
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