Trigonometric functions are incredibly important in mathematics and have wide-ranging applications. They are often used to study and understand periodic phenomena, such as waveforms or oscillations. Key trigonometric functions include sine (sin), cosine (cos), and tangent (tan), along with their reciprocal functions cosecant (csc), secant (sec), and cotangent (cot).

Properties of Trigonometric Functions:

• Definitions: The sine function (sin) relates the ratio of the length of the side opposite to an angle to the hypotenuse in a right triangle. The cosine function (cos) relates the ratio of the length of the side adjacent to an angle to the hypotenuse. And tangent (tan) is the ratio of the sine to the cosine.

• Graphs: The graphs of trigonometric functions are periodic, meaning they repeat themselves over regular intervals. The sine and cosine functions have a period of 2π radians or 360 degrees, while the tangent function has a period of π radians or 180 degrees. The amplitude refers to the maximum value of the function.

• Identities: Trigonometric identities are equations that are true for all possible values of the variables involved. These identities are crucial for solving trigonometric equations and simplifying expressions. Some important identities include the Pythagorean identities, sum and difference identities, double-angle identities, and half-angle identities.