Laboratory Test I  

(Section : 2)

For students with odd PC numbers

1.Write a program that takes as input from the user an angle  x in degrees (-90° ≤ x  ≤ 90°) and an integer N (1 ≤N ≤ 1000) and prints the value of  sin(x), by adding the first N  terms in its series expansion:                       

 

                                

 

First convert degree into radians (the value of x in the power series is in radians). You can use macro M_PI, where  approximate value of П is defined. For this purpose, you must include math.h

Also print the value of sin(x) using the standard library function.

Note: Include error check for input bounds.  Do not use library function pow() . Also do not use any arrays.

TEST CASES:

x N Sin(x)
180°  500  Incorrect input
 45°    3 0.707143
 45°    100 0.707107
75°    10 0.965926
90°    10 1.000003

                            

[MARKS :12]

2. Write a program that prints the largest 4 digit prime number.                                                         [MARKS :08]

 

 

For students with even  PC numbers


1.
Write a program that reads the value of x (real number, | x| <1) and a integer N (1 N ≤ 1000) and prints the value of log(1 + x), by adding the first N  terms in its series expansion:  

                       

Also print the value of log(1+x) using the standard library function. For this purpose, you must include math.h

Note: Include error check for input bounds. Do not use library function pow() . Also do not use any arrays.

 

TEST CASES:

x N log(1+x)
 -2 100 incorrect input
0.2 1000 0.182322
0.7 10 0.529532
0.7 500 0.530628

                                                                                                                                                                                     [MARKS :12]

2. Write a program to find the prime factors of a given number N.                                                  

TEST CASES:

Input(N) Prime factors
-8 incorrect input
10 2, 5
36 2, 3
420 2 , 3,  5, 7 

                 [MARKS :08]