Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. The primary functions are sine, cosine, and tangent, which are often abbreviated as sin, cos, and tan. These functions are essential in various fields, including geometry, physics, and engineering, as they help describe periodic phenomena, such as waves and oscillations. In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse, while the cosine is the ratio of the adjacent side to the hypotenuse. The tangent function, on the other hand, is the ratio of the opposite side to the adjacent side. These relationships