inverse trig functions

In the previous post we have discussed about Trigonometric Equations and In today's session we are going to discuss about inverse trig functions.  In trigonometry we also use trigonometrically function, so here we are going to discuss the inverse trig functions. They are sometimes called Cyclometric function. Limited opposite functions for trigonometric functions are the inverse trig function.
Let’s see how the inverse trigonometric functions are represented:
Function Inverse
Sin arcsin
Cos arccos
Tan arctan
Sec arcsec
Cosec arccosec
Cot arccot
The notation sin ^-1, cos ^-1, etc are generally used for the arcsin, arccos etc. but sometimes they are not correct (know more about inverse trig functions, here)
The relationship between the inverse trigonometric function for the various arguments:
Complimentary angles:
Arccos y = ⊼ / 2 – arcsin y;
Arccot y = ⊼ / 2 – arctan y;
Arccsc y = ⊼ / 2 – arcsec y;
Negative arguments:
Arcsin (-y) = - arcsin y;
Arccos (-y) = ⊼ - arccos y;
Arctan (-y) = - arctan y;
Arccot (-y) = ⊼ - arccot y;
Arcsec (-y) = ⊼ - arcsec y;
Arccsc (-y) = - arccsc y;
Reciprocal arguments
Arccos (1 / y) = arcsec y;
Arcsin (1 / y) = arccsc y;
Arctan (1 / y) = ½ ⊼- arctan y = arccot y, if the value of ‘y’ is greater than zero;
Arctan (1 / y) = - ½ ⊼ - arctan y = - ⊼+ arccot y, if the value of ‘y’ is less than zero;
Arccot (1 / y) = ½ ⊼- arccot y = arctan y, if the value of ‘y’ is greater than zero;
Arccot (1 / y) = - 3 / 2 ⊼ - arccot y = ⊼+ arctan y, if the value of ‘y’ is less than zero;
Arcsec (1 / y) = arccos y;
Arccosec (1 / y) = arcsin y;

Arccos y = arcsin √ (1 – y2), this condition is satisfy if o ≤ y ≤ 1;
Arctan y = arcsiny
√ (y2+ 1)
Arcsin y = 2arcsin y
1 + √ (y2+ 1),

Arccos y = arcsin √ (1 + y2,
1 + y
This function will be satisfied if -1 ≤ y ≤ +1.
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