Cosine Calculator
Calculate cosine (cos) values for angles in degrees and radians with exact values for special angles
Calculate Cosine (cos)
Enter any real number for the angle
Quick Reference
Common angles:
0° → cos = 1
30° → cos = √3/2 ≈ 0.866
45° → cos = √2/2 ≈ 0.707
60° → cos = 1/2 = 0.5
90° → cos = 0
Cosine Results
Formula and Calculation
Formula: cos(x) = adjacent/hypotenuse
Input: 0°
Result: cos(0°) = 1.000000
Quadrant Analysis
Quadrant: 1 (cosine is positive)
Behavior: decreasing from 1 to 0
Range: -1 ≤ cos(x) ≤ 1
Period: 360° (2π radians)
Related Trigonometric Values
Function Properties
Special Angles
Cosine Properties
Domain: All real numbers
Range: [-1, 1]
Period: 360° (2π radians)
Even function: cos(-x) = cos(x)
Maximum value: 1 (at 0°, 360°, etc.)
Minimum value: -1 (at 180°)
Understanding the Cosine Function
What is Cosine?
Cosine is one of the fundamental trigonometric functions. In a right triangle, cosine of an angle is the ratio of the adjacent side to the hypotenuse.
Right Triangle Definition
For an angle θ in a right triangle: cos(θ) = adjacent/hypotenuse
Unit Circle Definition
On the unit circle, cosine represents the x-coordinate of the point where the terminal side of the angle intersects the circle.
Key Properties
Even Function
cos(-x) = cos(x)
Periodicity
cos(x + 360°) = cos(x)
Pythagorean Identity
sin²(x) + cos²(x) = 1
Complementary Angles
cos(90° - x) = sin(x)
Cosine in Different Quadrants
Quadrant I (0° to 90°)
Cosine is positive
Decreases from 1 to 0
Quadrant II (90° to 180°)
Cosine is negative
Decreases from 0 to -1
Quadrant III (180° to 270°)
Cosine is negative
Increases from -1 to 0
Quadrant IV (270° to 360°)
Cosine is positive
Increases from 0 to 1