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Which six functions are used in trigonometry?

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Diagram of a right triangle labeled with sides a, b, and hypotenuse c, alongside formulas for the six trigonometric functions-sine, cosine, tangent, cosecant, secant, and cotangent-each defined by ratios of the triangle's sides. — trigonometry Based on the definitions, various simple relationships exist among the functions. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

In mathematics, the six fundamental trigonometric functions represent the ratios of the sides of a right triangle. These functions are essential to the study of trigonometry and are defined as follows:

Sine (sin): The ratio of the opposite side to the hypotenuse.
Cosine (cos): The ratio of the adjacent side to the hypotenuse.
Tangent (tan): The ratio of the opposite side to the adjacent side.
Cosecant (csc): The ratio of the hypotenuse to the opposite side.
Secant (sec): The ratio of the hypotenuse to the adjacent side.
Cotangent (cot): The ratio of the adjacent side to the opposite side.

These functions can also be defined as circular functions using the coordinates of points on a unit circle. Because they are based on ratios, they are periodic and satisfy various identities derived from the Pythagorean theorem, such as $\sin^{2} θ + \cos^{2} θ = 1$ .123