Trigonometry

Trigonometric Functions in C

<math.h> provides the standard trig functions. All angles are in radians, not degrees.

Functions

Degrees to Radians

To convert degrees to radians, multiply by π/180:

double deg = 90.0;
double rad = deg * M_PI / 180.0;
printf("%.4f\n", sin(rad));  // 1.0000

Key Values to Know

sin(0)     = 0       sin(π/6) = 0.5    sin(π/2) = 1
cos(0)     = 1       cos(π/3) = 0.5    cos(π/2) = 0
tan(π/4)   = 1

Using atan2 for Angles

atan2(y, x) is the robust way to get the angle of a 2D vector — it handles all quadrants:

// Angle of the vector (1, 1) = 45° = π/4
double angle = atan2(1.0, 1.0);
printf("%.4f\n", angle);          // 0.7854
printf("%.4f\n", angle * 4.0);    // 3.1416 (π)

Distance Between Two Points

The Euclidean distance formula: $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

double dx = 3.0, dy = 4.0;
double dist = sqrt(dx*dx + dy*dy);  // 5.0 (classic 3-4-5 triangle)

Your Task

Using <math.h>, compute and print with %.4f:

1. sin(M_PI / 6.0) (sine of 30°)
2. cos(M_PI / 3.0) (cosine of 60°)
3. atan2(1.0, 1.0) * 4.0 (reconstructing π)