August 20, 2014

Homework Help: Precalculus

Posted by Anon on Friday, January 20, 2012 at 3:42pm.

The figure shows part of a curve traced by a point on the circumference of a circle of radius 4 that rotates, without slipping, around a fixed circle of radius 2. The rotating circle starts with angle t = 0 radians and the point P (x, y) at (10, 0). In this problem you will find parametric equations of the resulting epicycloid.

In the figure, t = 0.9 radian. Find the coordinates (rounded to the nearest hundredth) of the center of the large moving circle.

Because the big circle rotates wtihout slipping, arc a on the big circle equals arc a on the small circle. Find a when t = 0.9 radian, as in the figure. Use the answer to find the measure of angle A that subtends arc a on the big circle.
a = units
angle A = radians

Angle θ at the center of the big circle has measure equal to t + A. Find θ when t = 0.9 radian. θ = radians.

Use the answers above to find the coordinates of point P when t = 0.9. (Round to the nearest hundredth).
( , )

In general, what does θ equal as a function of t?
θ = t

By repeating the process you used to arrive at the coordinates of point P when t = 0.9, write parametric equations for x and y as functions of t.

How many revolutions of t are needed to generate the entire graphs?

Diagram can be found blondebeliever.tumblr.[com]/precalc (on my blog) under question 3!

Answer this Question

First Name:
School Subject:

Related Questions

calculus - a circle of radius 1 rolls around the outside of a circle of radius 2...
calculus - a circle of radius 1 rolls around the outside of a circle of radius 2...
maths - O is the centre of the circle and A and B are points on the ...
Math - What is the approximate circumference of a circle with a radius of 6 ...
math - HELP!! the area A of the circle in the figure can be represented by A(r)=...
Math - Circle C has radius 4 inches. Circle D had radius 9 inches. These two ...
Algebra - The Circumference and area of a circle of radius r are givin by 2 [pie...
physics - A block of mass m = 4.30 kg is released from rest from point circle a ...
Physics - Three point charges, -6.35 10-9 C, -8.20 10-9 C, and +7.75 10-9 C, are...
triggg - Suppose a circle has a radius of 4.5 inches. If you double the radius ...