Sunday

November 23, 2014

November 23, 2014

Posted by **stan** on Saturday, August 28, 2010 at 10:52pm.

x= r(deta - cos deta)

Y= r(1- sin deta)

deta= pie/3

- calculus help please -
**MathMate**, Sunday, August 29, 2010 at 10:36am%pi;/3 is not correct. There is a value of θ for the horizontal tangent, and another for the vertical tangent.

Given:

x= r(θ - cos θ)

Y= r(1- sin θ)

For the given parametric equations, r is a magnification factor, so for all intents and purposes, we can assume it to be 1.0. If it assumes any other value, the graph will be magnified or reduced accordingly.

To find dy/dx or dx/dy, we can apply the chain rule

dy/dx = (dy/dθ) / (dx/dθ)

and similarly

dx/dy = (dx/dθ) / (dy/dθ)

where dx/dθ = r(1+sinθ), and

dy/dθ = r(-cosθ)

A vertical tangent occurs at a point where dy/dx=0, and a horizontal tangent occurs where dx/dy=0.

Note that at θ=-π/2, both dx/dθ and dy/dθ are zero. Use l'hôpital's rule to evaluate.

You should get a complete cycle if you work with θ from -2π to 2π.

To help you visualize the function, I include two graphics plots:

http://img411.imageshack.us/img411/5971/1283050369a.png

http://img690.imageshack.us/img690/6584/1283050369b.png

Post your results for verifications if you wish.

**Answer this Question**

**Related Questions**

calculus help - Find the points where the tangent line is horizontal or vertical...

Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...

calculus - Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) ...

calculus - 1. Consider the function f(x) = X^(4/3) +4x^(1/3) on the interval -8...

calculus - 1. Consider the function f(x) = X^(4/3) +4x^(1/3) on the interval -8...

Calculus - Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...

Calculus - Use the given equation to answer the following questions. (Enter your...

Calculus - the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a...

Calculus - For the parametric curve defined x=2t^3-12t^2-30t+9 and y=t^2-4t+6 .....

math - question: find the points at which the graph of x^2 -4x + y62 -6y =12 has...