2.1 Traversing Circles
Activity 2.1.2
Consider the circle pictured in Figure 2.1.6 that is centered at the point (2, 2) and that has circumference Assume that we track the -coordinate (that is, the height,
a. How far along the circle is the point
b. Label the subsequent points in the figure
c. Determine the
d. By plotting the points in Table 2.1.8 and connecting them in an intuitive way, sketch a graph of
e. What is similar about your graph in comparison to the one in Table 2.1.5? What is different?
f. What will be the value of
Show Solution
a. Since there are 8 segments in this circle and the circumference is 8, the distance from each point to the next is 1.
b.
To find the
So the radius is
For
c.
The
d.
e. It has clear periodic peaks and troughs, but does not touch the
f. For
For
A weight is placed on a frictionless table next to a wall and attached to a spring that is fixed to the wall. From its natural position of rest, the weight is imparted an initial velocity that sets it in motion. The weight then oscillates back and forth, and we can measure its distance,
a. Determine the period
b. What is the furthest distance the weight is displaced from the wall? What is the least distance the weight is displaced from the wall? What is the range of
c. Determine the average rate of change of
d. Based on the periodicity of the function, what is the value of
Show Solution
a.
b. The furthest distance is 13 (largest
Range:
c. SKIP
d.