Sections 0101, 0102, 0103 and Honors, Fall 1995

A Step by Step Plan for Project 2

The Step by Step Plan

1. Write a program with a for loop that prints out:

       Table of Sines
   
       sin(  0) = ????     sin(  5) = ????     sin( 10) = ????     
       sin( 15) = ????     sin( 20) = ????     sin( 25) = ????     
       sin( 30) = ????     sin( 35) = ????     sin( 40) = ????     
       sin( 45) = ????     sin( 50) = ????     sin( 55) = ????     
       sin( 60) = ????     sin( 65) = ????     sin( 70) = ????     
       sin( 75) = ????     sin( 80) = ????     sin( 85) = ????     
       sin( 90) = ????     sin( 95) = ????     sin(100) = ????     
       sin(105) = ????     sin(110) = ????     sin(115) = ????     
       sin(120) = ????     sin(125) = ????     sin(130) = ????     
       sin(135) = ????     sin(140) = ????     sin(145) = ????     
       sin(150) = ????     sin(155) = ????     sin(160) = ????     
       sin(165) = ????     sin(170) = ????     sin(175) = ????     
       sin(180) = ????     sin(185) = ????     sin(190) = ????     
       sin(195) = ????     sin(200) = ????     sin(205) = ????     
       sin(210) = ????     sin(215) = ????     sin(220) = ????     
       sin(225) = ????     sin(230) = ????     sin(235) = ????     
       sin(240) = ????     sin(245) = ????     sin(250) = ????     
       sin(255) = ????     sin(260) = ????     sin(265) = ????     
       sin(270) = ????     sin(275) = ????     sin(280) = ????     
       sin(285) = ????     sin(290) = ????     sin(295) = ????     
       sin(300) = ????     sin(305) = ????     sin(310) = ????     
       sin(315) = ????     sin(320) = ????     sin(325) = ????     
       sin(330) = ????     sin(335) = ????     sin(340) = ????     
       sin(345) = ????     sin(350) = ????     sin(355) = ????     
       sin(360) = ????     
       

2. Write a separate program that takes an angle in degrees from the user and prints out the equivalent angle in radians.

3. Modify the previous program to print out the value

   	x - x*x*x/6 + x*x*x*x*x/120
        

   where x is size of the angle in radians. This is very roughly the sine of the angle, since it uses only the first 3 terms of Taylor series.

4. Modify the program again. This time take another value from the user, call it n.
   Write a for loop that calculates the value of x raise to the n-th power.
   Write a for loop that calculates (2*n - 1) factorial.
   Write a boolean expression that will tell you if the n-th term is positive or negative.
   Check the answers with a calculator.

5. Put the loops and the boolean expression in the previous step into one giant loop that iterates n from 1 to 8. (So, you don't want to get n from the user anymore.) Then, you can sum all the terms together and get the Taylor series approximation.
   Check your answer on a calculator.

6. Modify the previous program so that the number of terms is entered by the user (instead of being the constant 8).

7. Put the giant for loop inside the for loop in step 1. (Of course, now you shouldn't ask the user which angle to use.)

8. Clean up your program (indentation, comments etc.) and you are done.