The cosine function, often abbreviated as cos, is one of the primary trigonometric functions. It relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. The cosine function is periodic and defined for all real numbers, making it a fundamental function in trigonometry.
The values of the angles associated with the cosine function can be categorized based on key angles, which include:
- 0 degrees (0 radians): The cosine of 0 is 1.
- 30 degrees (π/6 radians): The cosine of 30 degrees is √3/2.
- 45 degrees (π/4 radians): The cosine of 45 degrees is √2/2.
- 60 degrees (π/3 radians): The cosine of 60 degrees is 1/2.
- 90 degrees (π/2 radians): The cosine of 90 degrees is 0.
Beyond these specific angles, the cosine function continues to repeat its values due to its periodic nature. The cosine function has a period of 360 degrees (or 2π radians). This means that the values will repeat every full rotation:
- 270 degrees (3π/2 radians): The cosine of 270 degrees is 0.
- 360 degrees (2π radians): The cosine of 360 degrees is 1.
To summarize, the cosine function has specific values for standard angles, and these values can be used to solve a variety of problems in trigonometry and geometry.