
Trigonometry 



Trigonometric
Functions and Inverse Trigonometric Functions 
Trigonometric
functions graphs and relations 
The
sine function and the cosine function graphs and relations 
The
tangent function and the cotangent function graphs and relations 
The
cosecant function
and the
secant function graphs and relations 
The
cosecant function y
= csc x 
The graph of the cosecant
function 
The
secant function
y
= sec x 
The graph of the secant
function 





Trigonometric
functions and inverse trigonometric functions or
arcfunctions 
Trigonometric
functions graphs and relations 
Trigonometric
(cyclometric) 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
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
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
tangent function
y
= tan x
is the ratio of the ycoordinate to
the xcoordinate
of the terminal point of the arc x
of the unit circle, or it is the ratio of the sine function to the cosine function. 
In
a rightangled triangle the
tangent function is equal to the ratio of the length of the side
opposite the given angle to that of the adjacent side. 

 The
cotangent function
y
= cot x
is the reciprocal of the tangent function, or it is the ratio of the cosine
function to the
sine function. 
In
a rightangled triangle the cotangent function is equal to the ratio of the length of the side adjacent
to the given angle to that of the side opposite it. 




 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 










Precalculus contents
G 



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