A community for students.
Here's the question you clicked on:
 0 viewing
sassieston
 one year ago
Please help, Simmons, page 579 problem 4.
Prove that r1=theta and r2=1/theta intersect orthogonally at theta=1.
Pt 1: they intersect, r = 1 = 1/1 which is true.
Pt 2: Define psi1 as the angle between the line from the origin to a point on r=theta and the tangent to that point.
tan(psi1) = r1/(dr1/dtheta) = theta/1 = theta.
tan(psi2) = theta
orthonogal implies tan(psi1psi2) = 1
(since psi2 is negative)
this becomes:
(tan(psi1)tan(psi2))/(1+tan(psi1)tan(psi2)) = 1
2theta/(1theta^2) = 1
using theta=1,
2/0 = 1, which is false what am i doing wrong here?
sassieston
 one year ago
Please help, Simmons, page 579 problem 4. Prove that r1=theta and r2=1/theta intersect orthogonally at theta=1. Pt 1: they intersect, r = 1 = 1/1 which is true. Pt 2: Define psi1 as the angle between the line from the origin to a point on r=theta and the tangent to that point. tan(psi1) = r1/(dr1/dtheta) = theta/1 = theta. tan(psi2) = theta orthonogal implies tan(psi1psi2) = 1 (since psi2 is negative) this becomes: (tan(psi1)tan(psi2))/(1+tan(psi1)tan(psi2)) = 1 2theta/(1theta^2) = 1 using theta=1, 2/0 = 1, which is false what am i doing wrong here?

This Question is Closed

sassieston
 one year ago
Best ResponseYou've already chosen the best response.0dw:1373741004309:dw

sassieston
 one year ago
Best ResponseYou've already chosen the best response.0found out my mistake: tan(theta)=1 implies theta = 45 degrees, not 90
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.