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3.3. Math Functions¶
In mathematics, you have probably seen functions like \(\sin\) and \(\log\), and you have learned to evaluate expressions like \(\sin(\pi/2)\) and \(\log(1/x)\). First, you evaluate the expression in parentheses, which is called the argument of the function. For example, \(\pi/2\) is approximately 1.571, and \(1/x\) is 0.1 (if \(x\) happens to be 10).
Then you can evaluate the function itself, either by looking it up in a table or by performing various computations. The \(\sin\) of 1.571 is 1, and the \(\log\) of 0.1 is -1 (assuming that \(\log\) indicates the logarithm base 10).
This process can be applied repeatedly to evaluate more complicated expressions like \(\log(1/\sin(\pi/2))\). First we evaluate the argument of the innermost function, then evaluate the function, and so on.
C++ provides a set of built-in functions that includes most of the mathematical operations you can think of. The math functions are invoked using a syntax that is similar to mathematical notation:
This program performs calculations using some of the built-in functions from the cmath library.
The first example sets log to the logarithm of 17, base \(e\). There
is also a function called
log10 that takes logarithms base 10.
The second example finds the sine of the value of the variable angle.
C++ assumes that the values you use with
sin and the other trigonometric
tan) are in radians.
To convert from degrees to radians, you can divide by 360 and multiply by 2 * pi.
If you don’t happen to know \(\pi\) to 15 digits, you can calculate
it using the
acos function. The arccosine (or inverse cosine) of -1 is
\(\pi\), because the cosine of \(\pi\) is -1.
This program also uses built-in functions from the cmath library, specifically the functions that deal with angles. As you can see, we have a line of code that converts the default radians value to degrees.
Before you can use any of the math functions, you have to include the math header file. Header files contain information the compiler needs about functions that are defined outside your program. For example, in the “Hello, world!” program we included a header file named iostream using an include statement:
#include <iostream> using namespace std;
iostream contains information about input and output (I/O) streams,
including the object named
cout. C++ has a powerful feature called
namespaces, that allow you to write your own implementation of cout. But
in most cases, we would need to use the standard implementation. To
convey this to the compiler, we use the line
using namespace std;
As a rule of the thumb, you should write
using namespace std; whenever
you use iostream.
Similarly, the math header file contains information about the math functions. You can include it at the beginning of your program along with iostream:
Such header files have an initial ‘c’ to signify that these header files have been derived from the C language.