Mathematical library

It may be necessary in a program to use common mathematical functions such as the sine, square root, or log of a number. There are some standard methods Java provides to do this simply. To calculate y = x² it is easiest to use the expression y = x*x, however for higher powers of x this is awkward, so in general y = xⁿ is calculated using y = Math.pow(x,n).

The values or variables placed in the round brackets, (), are known as arguments.

These useful methods providing mathematical functions exist:

Math.E              // e as a double
Math.PI             // pi as a double 
Math.sin(x)         // sine of x
Math.cos(x)         // cosine of x
Math.tan(x)         // tangent of x
Math.asin(x)        // arcsine of x
Math.acos(x)        // arcsine of x
Math.atan(x         // arctangent of x
Math.exp(x)         // exponential of x
Math.log(x)         // natural logarithm of x
Math.pow(x,n)       // x raised to the power n (both double)
Math.sqrt(x)        // square root of x
Math.random()       // random double between 0.0 and 1.0 (uniform distribution)
                            // requires no argument
Math.abs(x)         // the absolute value of x, works for int, long, float and
                            // double values, returning value of the same type

Except Math.abs() these mathematical functions all give result values of type double. They also all take a double variables or values as their arguments -- both x and n in the above are double variables. Note that Math.pow() requires two arguments, whereas Math.random() requires none, although the brackets must still be included. Using Math.abs() is slightly different -- using it on a float variable will give a float value, on an int variable will return an int value, and so on.

Note that all the trigonometric functions work in radians.

Exercise 2.1

(6 marks)

Write a program that reads in a value for an angle from the keyboard, computes and writes out the sine and cosine and, as a check, the value of sin²x + cos²x for that angle. The value of sin²x + cos²x, of course, should be very close to 1. In your laboratory notebook, record the results of entering the angles 3.5 and 2.3e-3. You should use variables of type double and include all significant figures in your written answer. Stick a print out of your program in your lab notebook.