Trigonometric Functions

Last Updated : 9 Feb, 2026

Trigonometric Functions, often simply called trig functions, are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides. There are six basic trigonometric functions used in Trigonometry, which are:

The image added below shows a right-angle triangle PQR.

👁 hypotenuse

Then the six basic trigonometric functions formulas for this right-angle triangle are,

Function	Sides	Description	Relation
sin θ	PQ/PR	Perpendicular/Hypotenuse	sin θ = 1/cosec θ
cos θ	QR/PR	Base/Hypotenuse	cos θ = 1/sec θ
tan θ	PQ/QR	Perpendicular/Base	tan θ = 1/cot θ
sec θ	PR/QR	Hypotenuse/Base	sec θ = 1/cos θ
cosec θ	PR/PQ	Hypotenuse/Perpendicular	cosec θ = 1/sin θ
cot θ	QR/PQ	Base/Perpendicular	cot θ = 1/tan θ

Properties of Trigonometric Functions

Some of the common properties of trigonometric functions are discussed below:

Period refers to the length of one complete cycle of a trigonometric function, after which the function repeats.

Sine (sin), Cosine (cos), Secant (sec), Cosecant (csc): Period = 2π
Tangent (tan), Cotangent (cot): Period = π

Symmetry refers to the property that describes how the function behaves under reflection, translation, or rotation.

Even Functions: f(−θ) = f(θ) (Cosine and Secant).
Odd Functions: f(−θ) = −f(θ) (Sine, Tangent, Cosecant, Cotangent).

Learn in detail

Trigonometric Ratios
Trigonometric Values
Graph of Trigonometric Functions
Domain and Range of Trigonometric Functions
Differentiation of trigonometric function
integration of the trigonometric function

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