Question

find the locations where the tangent line to r=theta is vertical on [0,2pi]

Answer 1

r= what theta, sin theta, cos theta, tan theta. ???????????

Answer 2

just theta

Answer 3

the graph looks like a spiral

Answer 4

\[\frac{dy}{dx}=\frac{\frac{dr}{d \theta} \sin(\theta)+r \cos(\theta)}{\frac{dr}{d \theta} \cos(\theta)-rsin(\theta)}\]

Answer 5

so you need to find when the bottom is 0

Answer 6

thank you

Answer 7

http://tutorial.math.lamar.edu/Classes/CalcII/PolarTangents.aspx
good notes to have

Answer 8

honestly I'm having trouble finding where
\[\cos(\theta)-\theta \sin(\theta)=0 \]

Answer 9

have you solved it?

Answer 10

http://www.wolframalpha.com/input/?i=cos%28theta%29-theta+*sin%28theta%29%3D0
according to wolfram we should get these
but i think we have to use a numerical approach instead of an algebraic one