Trigonometric functions play a crucial role in mathematics, especially in the fields of geometry and algebra. These functions, including cosine, sine, and tangent, help describe the relationships between the angles and sides of triangles. Understanding how these functions work and how to use them is essential for solving various mathematical problems.

Cosine Function

The cosine function, often denoted as “cos,” represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle. In the unit circle, cosine measures the x-coordinate of a point on the circle. This function is periodic with a period of 2π radians, meaning it repeats its values every 360 degrees.

Sine Function

The sine function, denoted as “sin,” calculates the ratio of the opposite side to the hypotenuse of a right-angled triangle. On the unit circle, sine measures the y-coordinate of a point on the circle. Like cosine, sine is also periodic with a period of 2π radians, repeating every 360 degrees.

Tangent Function

The tangent function, represented as “tan,” is the ratio of the sine to the cosine function. It describes the angle’s slope and is also periodic with a period of π radians. The tangent function becomes undefined where the cosine function equals zero, leading to vertical asymptotes on its graph.

In summary, cosine, sine, and tangent functions are fundamental to trigonometry and are widely used in various applications, from engineering to physics. Mastery of these functions allows for a deeper understanding of wave behavior, oscillations, and other phenomena.