Lesson 8.9. Mathematical functions in C

math.h

The standard library math.h contains about a dozen common mathematical functions like

• cosine
• sine
• tangeant
• power
• square root
• exponential
• logarithmic
• ...

#include <math.h>

All functions that involve angles use the radian as a unit.

List of functions in math.h

The list of functions can be found on the page Wikipedia of math.h. Here are some of the most common ones:

// Sine of X
double sin(double X);

// Cosine of X
double cos(double X);

// Tangeante of X
double tan(double X);

// Arcsin(X) in domain [-π/2, π/2], x[-1, 1]
double asin(double X);

// Arccos(X) in domain [0, π], x[-1, 1]
double acos(double X);

// Arctan(X) in domain [-π/2, π/2]
double atan(double X);

// arc tangent of the quotient of its arguments (in the right quadrant)
double atan2( double Y, double X);

// Exponential of X
double exp(double X);

// Natural logarithm: ln(X), X>0
double log(double X);

// Base 10 logarithm: log10(X), X>0
double log10(double X);

// X exposant Y (X power Y)
double pow(double X, double Y);

// Square root of X, X>=0
double sqrt(double X);

// Absolute value of X : |X|
double fabs(double X);

// Rounded down to the nearest integer
double floor(double X);

// Rounded up to the nearest integer
double ceil(double X);

// Rounded to the nearest
double round(double X);

We will not detail each function, but only the atan2() function.

atan2

The function atan2() computes the arc tangeant on the basis of coordinates. In other words, atan2() computes the angle formed by a vector x,y and the x-axis.

Note the counter-intuitive order of the parameters: y first, then x.

Pi

The math.h library defines the symbolic constant M_PI which contains the value of \( \pi \):

#define M_PI       3.14159265358979323846

As long as the math.h library is included, this constant is accessible.

Example

The following example calculates the angle formed by the x,y vector and the x-axis.

x = 1
y = 0
atan2(0.00, 1.00) = 0.0000 rad

x = 1
y = 1
atan2(1.00, 1.00) = 0.7854 rad

Exercises

Exercise 1

Write a pythagoras() function that computes the length of the hypothenuse of a triangle from the length of the other two sides. Recall here the theorem of Pythagoras :

In a right triangle, the square of the length of the hypotenuse (or side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Opposite side = 4.0
Adjacent side = 3.0
hypotenuse = 5.00

#include <stdio.h> #include <math.h> // Calculate the length of the hypothenuse of a triangle // COMPLETE HERE int main(void) { // Ask the side length double oposite, adjacent; printf ("Opposite side = "); scanf ("%lf", &oposite); printf ("Adjacent side = "); scanf ("%lf", &adjacent); // Display the length of the hypotenuse printf ("Hypotenuse = %.2lf\n", pythagore(oposite, adjacent)); return 0; } // Calculate the length of the hypothenuse of a triangle // COMPLETE HERE

Exercise 2

Write a program that displays the coordinates of the points of a unit circle with a step of 20 degrees. Recall that the coordinates of the unit circle can be calculated by the following formulas:

$$ \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} cos(\alpha) \\ sin(\alpha) \end{bmatrix} $$

Display the points according to this example:

α=0.00   =>   [ 1.00 , y= 0.00]
α=0.35   =>   [ 0.94 , y= 0.34]
α=0.70   =>   [ 0.77 , y= 0.64]
α=1.05   =>   [ 0.50 , y= 0.87]
α=1.40   =>   [ 0.17 , y= 0.98]
α=1.75   =>   [-0.17 , y= 0.98]
α=2.09   =>   [-0.50 , y= 0.87]
α=2.44   =>   [-0.77 , y= 0.64]
α=2.79   =>   [-0.94 , y= 0.34]
α=3.14   =>   [-1.00 , y= 0.00]
α=3.49   =>   [-0.94 , y=-0.34]
α=3.84   =>   [-0.77 , y=-0.64]
α=4.19   =>   [-0.50 , y=-0.87]
α=4.54   =>   [-0.17 , y=-0.98]
α=4.89   =>   [ 0.17 , y=-0.98]
α=5.24   =>   [ 0.50 , y=-0.87]
α=5.59   =>   [ 0.77 , y=-0.64]
α=5.93   =>   [ 0.94 , y=-0.34]
α=6.28   =>   [ 1.00 , y=-0.00]

#include <stdio.h> #include <math.h> int main(void) { double x,y; double alpha; // Loop for the angle with a step of 20°. for ( /* COMPLETE HERE */) { // Calculate the x,y coordinates of the points // COMPLETE HERE // Display the point printf ("α=%.2lf => [%5.2lf , y=%5.2lf]\n", alpha, x, y); } return 0; }

Exercise 3

Write a function that calculates the distance between a point in space (x,y,z) and the origin:

// Calculate the norm of a vector
double norm(double x, double y, double z);

The main program asks the user to enter the coordinates of a point in the plane (X,Y) then the program displays the polar coordinates of this point:

X = 1.
Y = 2.
Argument = 1.11
Norm = 2.24

#include <stdio.h> #include <math.h> // Calculate the norm of a vector double norm(double x, double y, double z); int main(void) { double X,Y; // Ask for coordinates printf ("X = "); scanf ("%lf", &X); printf ("Y = "); scanf ("%lf", &Y); // Displays the polar coordinates // COMPLETE HERE return 0; } // Calculate the norm of a vector // COMPLETE HERE

Quiz

To calculate x², what can we use?

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If you have to use \( \pi \) in a program, how do you proceed?

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How to round a number down?

double x=-2.7;

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See also

• Learn C programming
• Lesson 1.1. History of C programming language
• Lesson 1.2. First program
• Lesson 1.3. Compilation
• Lesson 1.4. Preprocessor directives
• Lesson 1.5. Which compiler to choose?
• Lesson 1.6. Flowchart
• Lesson 2.1. Types and variables
• Lesson 2.2. Integers
• Lesson 2.3. Floating point numbers
• Lesson 2.4. Characters
• Lesson 2.5. Variables initialization
• Lesson 2.6. Ariane flight 501
• Lesson 3.1. Arithmetic operators
• Lesson 3.2. modulo
• Lesson 3.3. Operators and types
• Lesson 3.4. Type casting
• Lesson 3.5. Bitwise operators
• Lesson 3.6. Bitwise operators details
• Lesson 3.7. Shifting operators
• Lesson 3.8. Assignment operators
• Lesson 3.9. Increment and decrement operators
• Lesson 3.10. Comparison operators
• Lesson 3.11. Logical operators
• Lesson 3.12. Operator precedence
• Lesson 4.1. printf
• Lesson 4.2. scanf
• Lesson 4.3. putchar
• Lesson 5.1. Conditional branching (if...else)
• Lesson 5.2. Nested if and indentation
• Lesson 5.3. Checking intervals
• Lesson 5.4. Ternary Operator ?:
• Lesson 5.5. switch..case statement
• Lesson 5.6. Break keyword in switch..case
• Lesson 6.1. do..while loop in C
• Lesson 6.2. While loop in C
• Lesson 6.3. For loop in C
• Lesson 6.4. How to choose the right loop in C ?
• Lesson 6.5. Exercices on loops in C
• Lesson 7.1. Bit masking
• Lesson 7.2. Bit masking, how to clear a bit in C?
• Lesson 7.3. Bit masking, how to set a bit in C?
• Lesson 7.4. Bit masking, how to toggle a bit in C?
• Lesson 7.5. Bit masking, how to check a single bit in C?
• Lesson 7.6. Overview of bit masking
• Lesson 8.1. Basic syntax of C functions
• Lesson 8.2. Calling C functions
• Lesson 8.3. Void keyword
• Lesson 8.4. Return keyword
• Lesson 8.5. Variable scope
• Lesson 8.6. Global variables
• Lesson 8.7. Static variables
• Lesson 8.8. Random numbers in C
• Lesson 9.1. Syntax of C arrays
• Lesson 9.2. Array initialization
• Lesson 9.3. Multidimensional arrays
• Lesson 9.4. How C arrays are stored in memory?
• Lesson 9.5. Arrays and functions
• Lesson 9.6. Exercises on C arrays
• Lesson 10.1. Strings in C
• Lesson 10.2. Null terminated string
• Lesson 10.3. The string.h library
• Lesson 10.4. String and functions
• Lesson 11.1. Introduction to pointers in C
• Lesson 11.2. Syntax of C pointers
• Lesson 11.3. Dynamic memory allocation
• Lesson 11.4. Incrementing pointers
• Lesson 11.5. Pointers as function argument in C
• Lesson 12.1. Introduction to structures in C
• Lesson 12.2. Properties of structures in C
• Lesson 12.3. Structures and pointers
• Lesson 12.4. Structures and functions
• Lesson 13.1. Recursive functions in C
• Lesson 13.2. Depth of recursive functions
• Lesson 13.2. Mutual recursion
• Lesson 14.1. Additional exercises

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