May 27, 2015

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!

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