

The graphs of the
elementary functions 
Trigonometric
(cyclic) functions and inverse trigonometric functions (arc
functions) 
The
graphs of the trigonometric
functions and inverse trigonometric functions or arcfunctions 
The graph of
the
cosecant function 
The graph of
the
secant function 
The
graph of the
arccosecant and the
arcsecant function 





Trigonometric
(cyclic) functions and inverse trigonometric functions (arc
functions) 
Trigonometric functions are defined as the ratios of the sides of a right
triangle containing the angle equal to the argument of the
function in radians. 
Or
more generally for real arguments, trigonometric
functions are defined in terms of the coordinates of the
terminal point Q of
the arc
(or angle) of the unit circle with the initial point at P(1,
0). 



sin^{2}x
+ cos^{2}x
= 1 



The
graphs of the trigonometric
functions and inverse trigonometric functions or arcfunctions 
 The
cosecant function
y
= csc x
is the reciprocal of the sine function. 
In
a rightangled triangle the
cosecant function is equal to the ratio of the length of the
hypotenuse to that of the side opposite to the given angle. 

The
graph of the
cosecant function 



 The
secant function
y
= sec x
is the reciprocal of the cosine function. 
In
a rightangled triangle the secant function is equal to the
ratio of the length of the hypotenuse to that of the side
adjacent to the given angle. 

The
graph of the
secant 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 









Intermediate
algebra contents 



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