Question

You are given the polar curve r=1+cos(θ).

(a) List all of the points (r,θ) where the tangent line is horizontal. In entering your answer, list the points starting with the smallest value of r and limit yourself to r≥0 and 0≤θ<2π. If two or more points share the same value of r, list those starting with the smallest value of θ.
(b) List all of the points (r,θ) where the tangent line is vertical. In entering your answer, list the points starting with the smallest value of r and limit yourself to r≥0 and 0≤θ<2π. If two or more points share the same value of r, list those starting with the...

Answer 1

i can't understand what i'm doing wrong. dr/dtheta is -sin(theta) so the horizontal would be when dy/dx = 0. therefore\[0=-\sin(\theta)\sin(\theta)+(1+\cos(\theta))\cos(\theta)\]\[0= -\sin^2(\theta)+\cos(\theta)+\cos^2(\theta)\]

theta is pi/3. so r would be 1+cos(pi/3). but i plug that in and webwork says incorrect...

Answer 2

theta could also equal 5pi/3

Answer 3

Look at the graph and see if it can help you
http://www.wolframalpha.com/input/?i=polar+plot+r%3D1%2Bcos+theta&lk=4

Answer 4

no, it doesn't help, because i already did that....i have a graphing calculator

Answer 5

Look at that site
http://answers.yahoo.com/question/index?qid=20110104073559AAJ9Csa

Answer 6

that's exactly what i did....

Answer 7

i have theta is zero for horizontal at pi/3 and 5pi/3 and theta is zero for vertical at 0, 2pi/3, pi, 4pi/3, and 2pi...

Answer 8

1.) http://math.stackexchange.com/questions/466124/polar-curve-r-2-cos-theta-1
2.) http://cims.nyu.edu/~kiryl/Calculus/Section_9.3--Polar_Coordinates/Polar_Coordinates.pdf

Answer 9

Maybe these can help you out

Answer 10

not really, cause i'm pretty sure i did the steps right. i must have done something wrong in the math somewhere. i posted the steps above. i know how it's supposed to work. all you have to do is set dy/dx and dx/dy equal to zero to get the horizontal and vertical tangents. and yet, i'm getting the wrong answer. the first link you gave me was arc length. that has nothing to do with tangents. the second was just a summary of the same information i already have...i'm not trying to figure out HOW to do it, i'm trying to figure out what i did wrong.