- #1
xspook
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Homework Statement
Curve C is given in Polar Coordinates by the equation r=2+3sinθ.
Consider the usual Cartesian plane and take O as the pole and the positive x-axis as the polar axis.
Find points on the curve C where the tangent lines are horizontal or vertical and sketch the curve C.
Homework Equations
[itex]x^{2}[/itex]+[itex]y^{2}[/itex]=[itex]r^{2}[/itex]
x=rcosθ
y=rsinθ
tanθ=[itex]\frac{y}{x}[/itex]
The Attempt at a Solution
PART 1
For some reason I feel like the addition of 2 is throwing me off
r=2+3[itex]\frac{y}{r}[/itex]
[itex]r^{2}[/itex]=2+3y
[itex]x^{2}[/itex]+[itex]y^{2}[/itex]=2+3y
[itex]x^{2}[/itex]+[itex]y^{2}[/itex]-3y=2
[itex]x^{2}[/itex]+[itex]y^{2}[/itex]-3y+([itex]\frac{-3}{2})^{2}[/itex]=2+([itex]\frac{-3}{2})^{2}[/itex]
[itex]x^{2}[/itex]+(y-[itex]\frac{3}{2}[/itex][itex])^{2}[/itex]=[itex]\frac{17}{4}[/itex]??
I don't know where to go from the last line above for the center, maybe ([itex]\frac{3}{2}[/itex],0)??...
PART 2
I know also that I am supposed to take
[itex]\frac{∂r}{∂θ}[/itex] which is 3cosθ
when I take
[itex]\frac{∂x}{∂θ}[/itex] do I take the derivative of x=2+3([itex]\frac{y}{r}[/itex])([itex]\frac{x}{r}[/itex])?? And similarly for [itex]\frac{∂y}{∂θ}[/itex].
Lastly I know I have to take [itex]\frac{∂y}{∂x}[/itex] which I hope I can easily do after I sort out the issue above.
Thank you