 Transcendental functions - The graphs of transcendental functions Trigonometric (cyclometric) functions and inverse trigonometric functions (arc functions)
The graph of the sine function
The graph of the cosine function
The graph of the arc-sine function and the arc-cosine 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 graphs of the trigonometric functions and inverse trigonometric functions or arc-functions
-  The sine function  y = sin x is the y-coordinate 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 right-angled 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 x-coordinate 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 right-angled 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 arc-sine function  y = sin-1x 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-1x if and only if  x = sin y.  For example, Thus, the arc-sine 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 arc-cosine function  y = cos-1x 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-1x if and only if  x = cos y.  For example, Thus, the arc-cosine 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 arc-sine function and the arc-cosine function     College algebra contents B 