Transcendental functions - The graphs of transcendental functions
Trigonometric (cyclometric) functions and inverse trigonometric functions (arc functions)
The graph of the cosecant function
The graph of the secant function
The graph of the arc-cosecant and the arc-secant function
Transcendental functions - The graphs of transcendental functions
·  Trigonometric (cyclometric) 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).
 sin2x + cos2x = 1
-  The cosecant function  y = csc x is the reciprocal of the sine function.
In a right-angled 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 right-angled 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 arc-cosecant function  y = csc-1x 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-1x if and only if  x = csc y.  For example,
Thus, the arc-cosecant 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 arc-secant function  y = sec-1x 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-1x if and only if  x = sec y.  For example,
Thus, the arc-secant 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 arc-cosecant and the arc-secant function
College algebra contents B