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(b) Since semicircle ADB contains 180 , AD contains 180 (c) Since semicircle ACB contains 180 , BC contains 180

Implement the Indirect Selection Sort using an array of pointers. (See Problem 5.35.) Implement the Indirect Insertion Sort. (See Problem 5.36.) Implement the Indirect Random Shufie. (See Problem 5.15.) Rewrite the sum ( ) function (Example 6.15) so that it applies to functions with return type double instead of int. Then test it on the sqrt ( ) function (defined in <math. h>) and the reciprocal function. Apply the ~ riemann() function (Problem 6.30) to the following functions defined in

An angle is the figure formed by two rays with a common end point. The rays are the sides of the angle, while the end point is itsSvertex. The symbol for angle is / or ]; the plural is . S Thus, AB and AC are the sides of the angle shown in Fig. 1-8(a), and A is its vertex.

When the program is executed, the window will initially appear as shown in Fig. 5.12(a). Clicking on the Enable Oceans check box will cause the Oceans label to become active, as shown in Fig. 5.12(b). Also, clicking on the Display Seas check box will allow the Seas label to become visible.

cmath.h>: a. sqrt ( ), on the interval [l, 41; b . CO s ( ) , on the interval [0, n/2]; c. exp ( > , on the interval [0, 11; d . loa ( 1. on the interval 11, el.

An angle may be named in any of the following ways: 1. With the vertex letter, if there is only one angle having this vertex, as /B in Fig. 1-8(b). 2. With a small letter or a number placed between the sides of the angle and near the vertex, as /a or /1 in Fig. 1-8(c). 3. With three capital letters, such that the vertex letter is between two others, one from each side of the angle. In Fig. 1-8(d), /E may be named /DEG or /GED.

cmath.h>:

Fig. 1-8

a. sqrt(),atthepointx=4; b. sin(),atthepointx=n/6;

Fig. 18-8

Write the following function that returns the product of the n values jii l), f(2), . . . . and j(n). (See Example 6.15.)

int product(int (*pf)(int k), int n)

Only (b), (e), and (f) have reflectional symmetry. Note that when (d) is flipped, it will look like Fig. 18-9, which is different from the original in that the upper-left-hand crossing is horizontal instead of vertical.

Implement the Bisection A4ethod for solving equations. Use the following function:

Fig. 5.12(a)

Fig. 18-9

double root(double (*pf)(double x), double a, double b, int n)

If a pin were pushed through the origin on a graph and the paper were to be turned, the result would be a rotation about the origin. A rotation is described by the number of degrees by which the paper is turned. The 90 clockwise rotation (or 270 counter-clockwise) about the origin is given by P(x, y) A P (y, x). The 180 rotation about the origin is given by P(x, y) A P (x, y). The 270 clockwise (or 90 counter-clockwise) rotation about the origin is given by P(x, y) A P ( y, x). In general, the clockwise rotation about the origin of is given by P(x, y) A P (x cos y sin , y cos x sin )

Here, p f points to a function f that defines the equation f(x) = 0 that is to be solved, a and b bracket the unknown root x (i.e., a I x 2 b), and n is the number of iterations to use. For example, the call root(square,1,2,100) would return 1.414213562373095 ( = 42), thereby solving the equation x2 = 2. The Bisection Method works by repeatedly bisecting the interval and replacing it with the half that contains the root. It checks the sign of the product f(a) fib) to determine whether the root is in the interval [a, b].

Performing rotations Let triangle ABC be given by A(2, 1), B(3, 1), and C(3, 4). Graph the image of ^ABC as rotated about the origin by (a) 90 clockwise, (b) 180 , and (c) 270 clockwise.