Scan the angle in degrees x_deg (=60). Express this angle in
radians by using x=PI*x_deg/180, and calculate Y=cos(x) by
using the math.h library of functions.
Your objective in this quiz is to compare the so calculated
value of Y=cos(x) with the approximate value y obtained by
using 1, 2, 3, and 4 leading terms of the Taylor series:
cos(x) = 1-x^2/2! + x^4/4! - x^6/6! + ....
Recall that k!=k*(k-1)*(k-2)* ... *3*2*1 .
Use a do/while loop in conjunction with a switch statement
switch(). Enter an integer 1 for one term approximation,
2 for two terms, etc., by using scanf() function. Use
0 to exit the program.
Let your opening case calculate the fourth term -x^6/6!, let the
subsequent case calculate the x^4/4! term, etc. (In this way,
you wan't need to use a break statement within your switch).
Evaluate the corresponding y , print the result in one line,
and the relative error (y-Y)/Y in another line.
Execute your program for all four cases (with corresponding
printouts).
Scan the angle in degrees x_deg (=60). Express this angle in
radians by using x=PI*x_deg/180, and calculate Y=cos(x) by
using the math.h library of functions.
Your objective in this quiz is to compare the so calculated
value of Y=cos(x) with the approximate value y obtained by
using 1, 2, 3, and 4 leading terms of the Taylor series:
cos(x) = 1-x^2/2! + x^4/4! - x^6/6! + ....
Recall that k!=k*(k-1)*(k-2)* ... *3*2*1 .
Use a do/while loop in conjunction with a switch statement
switch(). Enter an integer 1 for one term approximation,
2 for two terms, etc., by using scanf() function. Use
0 to exit the program.
Let your opening case calculate the fourth term -x^6/6!, let the
subsequent case calculate the x^4/4! term, etc. (In this way,
you wan't need to use a break statement within your switch).
Evaluate the corresponding y , print the result in one line,
and the relative error (y-Y)/Y in another line.
Execute your program for all four cases (with corresponding
printouts).
............................................
Your output should look like this:
Enter x_deg: 60.
True value of cos(x) = 0.500000
Enter an integer 1-4; 0 to Exit
4
4 terms approximation
Approximate cos(x) = 0.499965
Relative error = -0.007 percent
Enter an integer 1-4; 0 to Exit
3
3 terms approximation
Approximate cos(x) = 0.501796
Relative error = 0.359 percent
Enter an integer 1-4; 0 to Exit
2
2 terms approximation
Approximate cos(x) = 0.451689
Relative error = -9.662 percent
Enter an integer 1-4; 0 to Exit
1
1 terms approximation
Approximate cos(x) = 1.000000
Relative error = 100.000 percent
Enter an integer 1-4; 0 to Exit
0