
Trigonometry 


Inverse Trigonometric Functions or
Arcfunctions and their Graphs 
The
arctangent function and the
arccotangent function 
The
arctangent function 
The
arccotangent function 
The
graph of the
arctangent function and the
arccotangent function 
The
arccosecant function and the arcsecant function 
The
graph of the
arccosecant and the
arcsecant function 





The
arctangent function and the
arccotangent function 
 The
arctangent function
y
= tan^{}^{1}x
or y
= arctan x
is the inverse of the tangent function, so that its
value for any
argument is an arc (angle) whose tangent equals the given
argument. 
That
is, y
= tan^{}^{1}x
if and only if x
= tan
y.
For
example, 


Thus, the arctangent
function is defined for all real arguments, and its principal
values are by
convention taken to be those strictly between p/2
and p/2. 

 The
arccotangent function
y
= cot^{}^{1}x
or y
= arccot x
is the inverse of the cotangent function, so that
its value for any
argument is an arc (angle) whose cotangent equals the given
argument. 
That
is, y
= cot^{}^{1}x
if and only if x
= cot
y.
For
example, 


Thus, the arccotangent
function is defined for all real arguments, and its principal
values are by
convention taken to be those strictly between 0
and p. 

The
graph of the
arctangent function and the
arccotangent function 


The
arccosecant function and the arcsecant function 
 The
arccosecant function
y
= csc^{}^{1}x
or y
= arccsc x
is the inverse of the cosecant function, so that its
value for any
argument is an arc (angle) whose cosecant equals the given
argument. 
That
is, y
= csc^{}^{1}x
if and only if x
= csc
y.
For
example, 


Thus, the arccosecant
function is defined for arguments less than 1
or greater than 1, and its principal
values are by
convention taken to be those between p/2
and p/2. 

 The
arcsecant function
y
= sec^{}^{1}x
or y
= arcsec x
is the inverse of the secant function, so that its value for any
argument is an arc (angle) whose secant equals the given
argument. 
That
is, y
= sec^{}^{1}x
if and only if x
= sec
y.
For
example, 


Thus, the arcsecant
function is defined for arguments less than 1
or greater than 1, and its principal
values are by
convention taken to be those between 0
and p. 

The
graph of the
arccosecant and the
arcsecant function 









Functions
contents D 



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