Functions and Recursive Functions - A Concise and Practical Introduction to Programming Algorithms in Java - page 81

the corresponding week day (”Sunday”, ..., ”Saturday”) to the output
console using a switch conditional statement.
Exercise 3.6 (Calculating sin nx and cos nx)

Write recursive functions sin(int n, double x) and cos(int n, double
x) that respectively compute sin nx and cos nx using the following
trigonometric formula:

sin( nx )=sin x cos( n − 1) x +cos x sin( n − 1) x,

cos( nx ) = cos x cos( n − 1) x − sin x sin( n − 1) x.

( Hint: Consider sin 0 = 0 and cos 0 = 1 as the terminal cases.)

Exercise 3.7 (Palindrome **)

A palindrome is a word or phrase that can be read in either direction
like “radar” or “Was it a rat I saw.” Write an iterative function
CheckingPalindrome(String str) that checks whether a word/phrase
stored in str is a palindrome or not. One shall use the charAt(int
pos) method of the String class that reports the character of type
char located at position pos in the string. Checking whether a string
is a palindrome or not can also be done recursively as follows: A
word s is a palindrome if there exists a word w and a character c
such that s = cwc and w is a palindrome (of smaller length). Design
a recursive function CheckingPalindromeRec(String str, int left,
int right) that checks whether the portion of the string str delimited
by the index range left and right is a palindrome or not. Test
your program by calling the function CheckingPalindromeRec(str, 0,
str.length()-1);