A trigonometric function refers to any of the mathematical functions that deal with the relationship between the angles and the sides of a right triangle. These functions are used extensively in the field of trigonometry and have significant applications in various branches of science, engineering, and mathematics.
Trigonometric functions include sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Each function is defined based on the ratio of two sides of a right triangle, namely the opposite side, adjacent side, and hypotenuse.
The sine function (sin) is defined as the ratio of the length of the side opposite to an angle to the length of the hypotenuse. The cosine function (cos) is defined as the ratio of the length of the side adjacent to an angle to the length of the hypotenuse. The tangent function (tan) is defined as the ratio of the sine to the cosine of an angle.
The other three trigonometric functions, cosecant (csc), secant (sec), and cotangent (cot), are the reciprocals of sine, cosine, and tangent, respectively. Cosecant (csc) is the ratio of the hypotenuse to the length of the side opposite to an angle. Secant (sec) is the ratio of the hypotenuse to the length of the side adjacent to an angle. Cotangent (cot) is the ratio of the cosine to the sine of an angle.
Trigonometric functions are characterized by their periodicity, meaning that their values repeat at regular intervals. They play a crucial role in solving non-right angle triangles, analyzing periodic phenomena, and modeling various natural phenomena such as sound waves, light waves, and oscillatory motions
