预备微积分 · 免费预览
圆周上的运动
一个沿圆周运动的点如何自然地产生一个函数？
1. Introduction
Introduction
2. Circular Functions
Circular Functions
3. Properties of Circular Functions
Properties of Circular Functions
4. Radius from circumference
A Ferris wheel has a circumference of 150 meters. What is its radius, in meters, to one decimal place?
5. Distance between evenly spaced points
A circle of circumference 8 units has 8 evenly spaced points. What is the distance between adjacent points along the circle?
6. Coordinates of a point on the circle
A circle centered at (2, 2) has circumference 8. What are the radius and the y-coordinate of the point directly below the center?
7. Shape of the height graph
The height of a point traversing the circle as a function of distance d has period 8, midline 2 and amplitude 4/pi. What is h(51)?
8. Height after many periods
A weight's distance from the wall is periodic with period 4 seconds, and f(2.75) = 12.619 inches. What is f(6.75)?
9. Period, midline and amplitude
A weight oscillates between 3 and 13 inches from the wall with a period of 4 seconds. What are its amplitude, midline and range?
10. Comparing two average rates of a weight
A weight's distance from the wall has average rates -4.772 in/s on [4, 4.25] and -1.524 in/s on [4.75, 5]. What do the values say?
11. The period reduces every later input
A periodic height function with period 8 has h(51) = h(3).