Trigonometric functions, also known as circular functions, are functions of an angle. They relate the angles of a triangle to the lengths of its sides.

Specifically, trigonometric functions relate an angle to the ratios of two sides of a right triangle. The basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

• Sine (sin): The ratio of the length of the opposite side to the length of the hypotenuse.
• Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse.
• Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side. It is also equal to sin(θ)/cos(θ).
• Cotangent (cot): The ratio of the length of the adjacent side to the length of the opposite side. It is also equal to cos(θ)/sin(θ), or 1/tan(θ).
• Secant (sec): The ratio of the length of the hypotenuse to the length of the adjacent side. It is also equal to 1/cos(θ).
• Cosecant (csc): The ratio of the length of the hypotenuse to the length of the opposite side. It is also equal to 1/sin(θ).

Trigonometric functions are used extensively in various fields, including mathematics, physics, engineering, and navigation.

More information can be found on these resources:

• Wikipedia - Trigonometric functions
• Khan Academy - Trigonometry