Inverse Trigonometry

Inverse Trigonometry | free study material for IITJEE , NDA and Air force | SAT | CBSE | SSAT | COOP

⚫Introduction
⚪ The inverse of a function f: A → B exists if f is one -one onto i.e. a bijection and is given by f(x) = y ⇒ f^-1(y) =x.
⚪ Consider the sine function with domain R and range [-1,1]. Clearly this function is not a bijection and so it is not invertible. If we restrict the domain of it in such a way that it becomes one-one , then it would become invertible. If we consider sine as a function with domain [-π/2, π/2 ] and co-domain [-1,1] , then it is a bijection and therefore , invertible. The inverse of sine function is defined as sin^-1x = θ where θ → [-π/2, π/2 ] and x → [-1,1]

⚫ Domain and range of trigonometry function
Domain and range of trigonometry function

⚫ Basic Formula of Inverse Trigonometry :
sin^-1(-x) = -sin^-1x
cos^-1(-x) = π -cos^-1x
tan^-1(-x) = -tan^-1x
cot^-1(-x) = π -cot^-1x
sec^-1(-x) = π -sec^-1x
cosec^-1(-x) = -cosec^-1x
sin^-1x + cos^-1x = π/2
tan^-1x + cot^-1x = π/2
sec^-1x + cosec^-1x = π/2

Practice set 1 Practice set 2 Practice set 3

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