The trigonometric functions, also called circular functions, are the sine, cosine, tangent, cotangent,
secant, and cosecant. For
a real angle 
, the sine and cosine
give the vertical and horizontal coordinates, respectively, of the corresponding
point on the unit circle. The remaining functions
are obtained from these by quotients and reciprocals:
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
The hyperbolic functions are closely related analogs obtained by removing factors of 
from the corresponding formulas in terms of 
. Two distinct generalizations associated with unit superellipses
are the p-trigonometric functions
and the area-parameterized squigonometric
functions. Other notations are sometimes used, as summarized in the following
table.
 | alternate notations |
 | 
(Erdélyi et al. 1981, p. 7),  (Gradshteyn and Ryzhik 2000, p. xxix) |
 |  (Gradshteyn and Ryzhik 2000, p. xxvii) |
 |  (Gradshteyn and Ryzhik 2000, p. xxix) |
The inverses of these functions (the inverse trigonometric functions) are denoted 
, 
, 
, 
, 
, and 
. Note that the 
notation here means inverse
function, not 
to the 
power.
