Show that the curve r=sin?tan? (called a cissoid of Diocles) has the line x=1 as

Q: Show that the curve r=sin?tan? (called a cissoid of Diocles) has the line x=1 as

r=sin(theta)*(tan(theta)) its cartesian equation is given by: y^2 = x^3/(1-x) so dy/dx=(3 x^2-2 x^3)/(2 (x-1)^2 y) so as x->1 slope tends to infinity so its asymptote

ID: 3287813 • Letter: S

Question

Show that the curve r=sin?tan? (called a cissoid of Diocles) has the line x=1 as a vertical asymptote. Show also that the curve lies entirely within the vertical strip 0?x<1. Use these facts to help sketch the cissoid. Okay, so I'm so confused on how to approach this problem. I know I'm supposed to discover that as the limit approaches infinity and negative infinity, I should get 1. However, I'm not sure if I should solve for theta or if I can even do it that way? Thanks so much for your help.

Explanation / Answer

r=sin(theta)*(tan(theta))

its cartesian equation is given by:

y^2 = x^3/(1-x)

so dy/dx=(3 x^2-2 x^3)/(2 (x-1)^2 y)

so as x->1

slope tends to infinity

so its asymptote

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Show that the curve r=sin?tan? (called a cissoid of Diocles) has the line x=1 as

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