The cosine function, commonly written as cos(θ), is a fundamental function in trigonometry that describes the relationship between the adjacent side and the hypotenuse of a right triangle. The values of the cosine function correspond to specific angles, which are often represented in degrees. Here are some key angles and their cosine values:
- 0°:
cos(0°) = 1 - 30°:
cos(30°) = √3/2 ≈ 0.866 - 45°:
cos(45°) = √2/2 ≈ 0.707 - 60°:
cos(60°) = 1/2 = 0.5 - 90°:
cos(90°) = 0 - 120°:
cos(120°) = -1/2 = -0.5 - 135°:
cos(135°) = -√2/2 ≈ -0.707 - 150°:
cos(150°) = -√3/2 ≈ -0.866 - 180°:
cos(180°) = -1 - 210°:
cos(210°) = -√3/2 ≈ -0.866 - 225°:
cos(225°) = -√2/2 ≈ -0.707 - 240°:
cos(240°) = -1/2 = -0.5 - 270°:
cos(270°) = 0 - 300°:
cos(300°) = 1/2 = 0.5 - 315°:
cos(315°) = √2/2 ≈ 0.707 - 330°:
cos(330°) = √3/2 ≈ 0.866 - 360°:
cos(360°) = 1
These cosine values are also cyclical, repeating every 360°. This means that for example, cos(360°) = cos(0°) = 1. The cosine function is especially important in various fields such as physics, engineering, and computer graphics, where waveforms and oscillations are often analyzed.
In the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate plane, the cosine of an angle can be interpreted as the x-coordinate of the point where the terminal side of the angle intersects the circle. This visual representation can provide deeper insight into the behavior of the cosine function as angles change.