Trigonometry

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 arc-functions
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).
 sin2x + cos2x = 1
-  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 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 tangent function  y = tan x is the ratio of the y-coordinate to the x-coordinate 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 right-angled 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 right-angled 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 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
Functions contents D