# TRIGONOMETRIC FUNCTIONS

In a right angled triangle ABC, ∠CAB = A and ∠BCA = 90° = π/2. AC is the base, BC the altitude and AB is the hypotenuse.

We refer to the base as the adjacent side and to the altitude as the opposite side. There are six trigonometric ratios, also called trigonometric functions or circular functions. With reference to angle A, the six ratios are:

is called sine of A , and written as sinA

is called the cosine of A , and written as cosA

is called the tangent of A , and written as tanA
Obviously, .
The reciprocals of sine, cosine and tangent are called the cosecant, secant and cotangent of A respectively. We write these as cosec A, sec A, cot A respectively.

Since the hypotenuse is the greatest side in a right angle triangle, sin A and cos A can never be greater than unity and cosec A and sec A can never be less than unity.

Notes:

• Above mentioned method relating trigonometric functions to angles and sides of a triangle is called geometric definition of trigonometric functions. One can define these functions in analytical ways without any reference to geometry, which is beyond the scope of this material. You just have to understand that the argument of these functions can also be a real number, not necessarily the angles only. You may refer to the chapter ‘Functions’ in Phase-II of RSM for detailed study of behaviour of these functions and their graphs.
• All the six trigonometric functions have got a very important property in common that is periodicity.
• Remember that the trigonometrical ratios are real numbers and remain same so long as the angles are real.

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