6.2.2c3.notebook
Nov. 6
November 06, 2013
6.2: Circular Motion and Periodic Functions
6.2.2: Modeling Circular Motion
How can the coordinates of any point on a rotating
circular object be determined from the radius and angle
of rotation?
1. Imagine that a small Ferris wheel has radius 1
decameter (about 33 feet)
and that your seat is at point A when the wheel begins to turn counterclockwise about
its center a point C.
a. How does the x­coordinate
of your seat change as the wheel turns?
b. How does the y­coordinate
of your seat change as the
wheel turns?
2. Find angles of rotation between 0o and 360o that will take the seat from point A to the following special points.
y
a. Maximum and minimum distance from the horizontal axis.
c
A
x
b. Maximum and minimum distance from the vertical axis.
c. Points with equal x­ and y­ coordinates.
d. Points with opposite x­ and y­ coordinates.
6.2.2c3.notebook
November 06, 2013
3. Find coordinates of points that tell the location of the Ferris wheel seat that begins at point
A(1,0) when the wheel undergoes the following rotations. Record the results on a sketch that
shows a circle and the points with their coordinate labels.
Definitions of trigonometric functions,
y
0o ≤ θ ≤ 360o
P(x,y)
sine of θ = sin θ = y/r
r
y
cosine of θ = cos θ = x/r
θ
O
x
Q
x
tangent of θ = tan θ = y/x (x ≠ 0)
6.2.2c3.notebook
November 06, 2013
4. When the Ferris wheel has rotated through an angle of 40o, the seat that started at A(1,0) will be at about A'(0.77, 0.64). Explain how the symmetry of the circle allows you to deduce the location of that seat after rotations of 140, 220, 320 degrees
and some other angles as well.