inverse circular functions

The circular functions are functions of an angle. They are important in the study of triangles and modeling periodic phenomena, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right triangle contai..

Theorem ..

Let f : A B be a real valued one-one and onto function. Therefore, we can define a function, (denoted by f - 1 ) called 'the inverse of f ' as follows: f - 1 : B A such that..

Other Circular Functions (Reciprocal functions of cos , sin and tan)..

Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric function. For ready reference, the domain and ran..

Which is the graph of a function and its inverse? => Graph 2 or Graph 1 or Graph 4 or Graph 3..

The Derivative of Inverse Trignometric Functions includes: 1. sin - 1 x, 2. cos - 1 x, 3. tan - 1 x, 4. cot - 1 x, 5. sec - 1 x, 6. cosec - 1 ..

Definition of sin - - 1 x For x [-1, 1], if q is an angle whose sine is x, then we say that sine inverse x is q and write sin -1 x = q . For practical purposes, only principal values of sin - 1 x are considered. sin - 1 x is a function of x with domain [-1,1] and range [- p /2, ..

Which pair of functions are not inverses? => f(x ) = 7 x + 14, g(x ) = 7 x - 4 or f(x ) = 2 x - 7, g(x ) = x + 7 2 or f(x ) = 7 x + 14, g(x ) = 1 7 x - 2 or f(x ) = x - 5, g(x ) = x + 5..

In the principle value branches, the following formulae holds: - sin -1 (sin x) = x - cos -1 (cos x) = x - tan -1 (tan x) = x - cos -1 (cot x) = x - sec -1 (secx) = x - cosec -1 (cosecx) = x - sin -1 (-x) = -sin -1 x - cos -1 (-x) = p - cos -1 x - t..