MATHEMATICAL FUNCTIONS, CHARACTERS, AND STRINGS - Introduction to Java Programming: Comprehensive Version - page 152

Here, s is the length of a side. Write a program that prompts the user to enter the
number of sides and their length of a regular polygon and displays its area. Here is
a sample run:

Enter the number of sides: 5
Enter the side: 6.5
The area of the polygon is 74.69017017488385

*4.6

( Random points on a circle ) Write a program that generates three random points
on a circle centered at (0, 0) with radius 40 and display three angles in a triangle
formed by these three points, as shown in Figure 4.7a. (Hint: Generate a random
angle

, as shown in Figure 4.7b and the point deter-
mined by this angle is (r*cos( a ), r*sin( a )).)

a in radians between 0 and 2

p

x = r × cos( α ) and y = r × sin( α ) 0 o'clock position

p 2

( x , y )

60

r

p 3

p 1

r

65

α

(0, 0)

55

p 4 p 5

(a) (b) (c)

F IGURE 4.7

(a) A triangle is formed from three random points on the circle. (b) A random
point on the circle can be generated using a random angle a . (c) A pentagon is centered at
(0, 0) with one point at the 0 o'clock position.

*4.7

( Corner point coordinates ) Suppose a pentagon is centered at (0, 0) with one point
at the 0 o'clock position, as shown in Figure 4.7c. Write a program that prompts
the user to enter the radius of the bounding circle of a pentagon and displays the
coordinates of the five corner points on the pentagon. Here is a sample run:

Enter the radius of the bounding circle: 100
The coordinates of five points on the pentagon are
(95.1057, 30.9017)
(0.000132679, 100)
(-95.1056, 30.9019)
(-58.7788, -80.9015)
(58.7782, -80.902)

Sections 4.3-4.6
*4.8

( Find the character of an ASCII code ) Write a program that receives an ASCII code
(an integer between 0 and 127 ) and displays its character. Here is a sample run:

Enter an ASCII code: 69
The character for ASCII code 69 is E