By Rafael Bombelli
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Extra resources for L’Algebra
Sample text
Our aim is to support, with examples and information, the effort to use computing to help learning. For calculus, the gveatest advantage of the computev is to o$er graphics. You see the function, not just the formula. As you watch, f ( x ) reaches a maximum or a minimum or zero. A separate graph shows its derivative. Those statements are not 100% true, as everybody learns right away-as soon as a few functions are typed in. But the power to see this subject is enormous, because it is adjustable.
What is their (shortest) period? 4 Show that cos 28 and cos28 have period n and draw them on the same graph. 5 At 8 = 3n/2 compute the six basic functions and check cos28 + sin28, sec20 - tan2 8, csc28 - cot28. , 7 The area of a circle is nr2. What is the area of the sector that has angle 8? It is a fraction of the whole area. 8 Find the distance from (1, 0) to (0, 1) along (a) a straight line (b) a quarter-circle (c) a semicircle centered at (3,i). 9 Find the distance d from (1,O) to a circle why 6d is less than 2n.
Choose the center point and press E N T E R. The new graph appears. Change those scaling factors with Z 0 0 M S e t F a c t o r s . Best of all, create your own viewing window. Press Z 0 0 M B o x . To draw the box, move the cursor to one corner. Press E N T E R and this point is a small square. The same keys move a second (blinking) square to the opposite corner-the box grows as you move. Press E N T E R, and the box is the new viewing window. The graphs show the same function with a change of scale.