Precalculus
posted by Anon .
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!

Precalculus 
Steve
Let r be the radius of the small inside circle
Let R be the radius of the large outside circle
Let C be the center of the large circle
Cx = (r+R)cos(t)
Cy = (r+R)sin(t)
a = rt
A = a/R
θ = t+A
Px = Cx + Rcosθ
Py = Cy + Rsinθ
r = 2
R = 4
when t = 0.9
Cx = 6cos.9 = 3.73
Cy = 6sin.9 = 4.70
a = 2t = 1.80
A = 1.8/4 = 0.45
θ = t+A = 1.35
Px = 3.73 + 4cos1.35 = 4.61
Py = 4.70 + 4sin1.35 = 8.60
Px = 6cost + 4cos3t/2
Py = 6sint + 4sin3t/2
After t has gone once around, the outer circle has only made a half turn. So, after 2 turns of t, we have 3 turns of A. 
Precalculus 
Steve
fooplot has a good app for xy plots, parametric plots, and polar plots
Respond to this Question
Similar Questions

physics
An object, after being released from its circular path, travels the distance OA in the same time it would have moved from O to P on the circle. The speed of the object on and off the circle remains constant at the same value. Suppose … 
maths
O is the centre of the circle and A and B are points on the circumference of the circle. The radians of the circle is 12 cm and the angle AOB is 54 degrees. Choose the one option which gives the length of the circle joining A and B … 
Algebra
The Circumference and area of a circle of radius r are givin by 2 [pie] r and [pie] r[2], respectively use 3.14 for the constant [pie] A. What is the circumference of a circle with a radius of 2 m? 
calculus
a circle of radius 1 rolls around the outside of a circle of radius 2 without slipping. the curve traced by a point on the circumfarence of the smaller circle is callled an epicycloid. use the angle theta to find a set of parametric … 
calculus
a circle of radius 1 rolls around the outside of a circle of radius 2 without slipping. the curve traced by a point on the circumfarence of the smaller circle is callled an epicycloid. use the angle theta to find a set of parametric … 
math
HELP!! the area A of the circle in the figure can be represented by A(r)=pi,r^2 where r is the radius what are the resonable domain and range for each function? 
Math
Circle C has radius 4 inches. Circle D had radius 9 inches. These two circles are connected. Point A,B,and E are points of tangency. Find AB. From point C to point D(which is the radius of circle C plus the raduis of circle D) it is … 
triggg
Suppose a circle has a radius of 4.5 inches. If you double the radius of the circle, does the area of the circle double as well? 
Math
What is the approximate circumference of a circle with a radius of 6 centimeters? 
Maths
1. In the xycoordinate plane, point A is the midpoint of the segment with endpoints (2,4) and (4,4). What is the distance from point A to the origin?