Trigonometry Ratios-Sine, Cosine, Tangent

 The trigonometric ratios of a triangle are also called the trigonometric functions. Sine, cosine, and tangent are 3 important trigonometric functions and are abbreviated as sin, cos and tan. Let us see how are these ratios or functions, evaluated in case of a right-angled triangle.

Consider a right-angled triangle, where the longest side is called the hypotenuse, and the sides opposite to the hypotenuse are referred to as the adjacent and opposite sides.

Six Important Trigonometric Functions

The six important trigonometric functions (trigonometric ratios) are calculated using the below formulas and considering the above figure. It is necessary to get knowledge about the sides of the right triangle because it defines the set of important trigonometric functions.

Functions	Abbreviation	Relationship to sides of a right triangle
Sine Function	sin	Opposite side/ Hypotenuse
Tangent Function	tan	Opposite side / Adjacent side
Cosine Function	cos	Adjacent side / Hypotenuse
Cosecant Function	cosec	Hypotenuse / Opposite side
Secant Function	sec	Hypotenuse / Adjacent side
Cotangent Function	cot	Adjacent side / Opposite side

Even and Odd Trigonometric Functions

The trigonometric function can be described as being even or odd.

Odd trigonometric functions: A trigonometric function is said to be an odd function if f(-x) = -f(x) and symmetric with respect to the origin.

Even trigonometric functions: A trigonometric function is said to be an even function, if f(-x) = f(x) and symmetric to the y-axis.

We know that

• Sin (-x) = – Sin x
• Cos (-x) = Cos x
• Tan (-x) = -Tan x
• Csc (-x) = – Csc x
• Sec (-x) = Sec x
• Cot (-x) = -Cot x

Therefore, cosine and secant are the even trigonometric functions, whereas sine, tangent, cosecant and cotangent are the odd trigonometric functions. If we know the even and odd trigonometric functions, it helps us to simplify the trigonometric expression when the variable inside the trigonometric function is negative.