Inverse Trigonometric Functions


Ask a Question, Get an Answer!
Hundreds of tutors are online and ready to help you right now!

Definition of sin

-1x

For x Î [-1, 1], if q is an angle whose sine is x, then we say that sine inverse x is q and write sin-1x = q.

For practical purposes, only principal values of sin-1x are considered.

sin-1x is a function of x with domain [-1,1] and range [-p/2, p/2].

The graph of sin-1x is as shown in the figure below.

Definition of cos

-1 x

cosine inverse x is q and write cos-1x = q.

In particular,

For practical purposes, only principal values of cos-1x are considered.

cos-1x is a function of x with domain [-1,1] and range [0, p].

The graph of cos-1x is as shown in the figure below.

Definition of tan

-1x

tangent inverse of x is q and write tan-1x = q.

In particular,

The graph of tan-1x is as shown in the figure below.

Definition of cot

-1x

For x Î R, if q is an angle whose cotangent is x, then we say that cotangent inverse of x is q and write cot-1x= q.

In particular,

For practical purposes, only principal values of cot-1x are considered.

Definition of sec

-1x

For x Î R - (-1, 1), if q is an angle whose secant is x, then we say that secant inverse of x is q and write sec-1x = q.

In particular,

For practical purposes, only principal values of sec-1x are considered.

sec-1x is a function of x with domain R-(-1,1) and range [0,p]-{p/2}.

Definition of cosec

-1x

For x Î R - (-1,1), if q is an angle whose cosecant is x, then we say that cosecant inverse of x is q and write cosec-1 x = q.

In particular, if q Î [-p/2, p/2] - {0}, then q is called the principal value of cosec-1 x.

For practical purposes, only principal values of cosec-1x are considered.

cosec-1x is a function of x with domain R-(-1,1) and range [-p/2, p/2]-{0}.

Note:

sin-1 x is only a symbol to denote sine inverse of x.

Table of domain and range of inverse trigonometric function

Relation between inverse functions:

Prove the following identities:

Proof:

Let,

Let,

Let,

Let,

Example 1:

Solve the following equation:

Suggested answer:

Example 2:

Prove the following equation:

Suggested answer:



Ask a Question? Get an Answer!

connect to a tutor


Related Searches

inverse trigonometry

;,  

trigonometric functions

,  

inverse functions

,  

inverse of a function

,  

inverse trigonometric functions

,  

Trigonometric formulae

,  

inverse of function

,  

inverse function

,  

inverse of functions

,  

graphing functions equation

,  

inverse of a function equation

,  

function graph relation

,  
definition of tangent
,  
domain and range
,  
definition
,  
domain
,  
how to find range?
,  
cosecant
,  
secant
,  
what is a secant
...more