Section 4.8– Number 6
Describe in words how the unit circle is traced out, including when the particle is
moving clockwise and when and where the particle is moving counter clockwise.
x = cos t
y = sin t
Solution:
The easiest way to do this is to make a table for t, x and y.
t
−2π
x
y
1
0
−
3π
2
−π
0
1
−1
0
−
π
0
π
1
0
0
1
2
0
−1
π
3π
2
2π
−1
0
0
−1
1
0
2
Plotting the (x, y) ordered pairs, we have
y
1
−1
1
x
−1
This describes the particle going in a counterclockwise direction for all t, it does not
change direction.