

The graphs of the
elementary functions 
Trigonometric
(cyclometric) functions and inverse trigonometric functions (arc
functions) 
The
graphs of the trigonometric
functions and inverse trigonometric functions or arcfunctions 
The graph of
the sine function 
The graph of
the
cosine function 
The graph of
the arcsine function and the arccosine 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
sine function
y
= sin x
is the ycoordinate
of the terminal point of the arc x
of the unit circle. The
graph of the sine function is the sine curve or sinusoid. 
In
a rightangled triangle the
sine function is equal to the ratio of the length of the side
opposite the given angle to the length of the hypotenuse. 

The
graph of the
sine
function 


 The
cosine function
y
= cos x
is the xcoordinate
of the terminal point of the arc x
of the unit circle. The
graph of the cosine function is the cosine curve or cosinusoid. 
In
a rightangled triangle the cosine function is equal to the
ratio of the length of the side adjacent the given angle to the
length of the hypotenuse. 

The
graph of the
cosine
function 



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


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

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


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

The
graph of the
arcsine
function and the arccosine
function 









Intermediate
algebra contents 



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