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# Inverse Trigonometric Functions

The inverse Trigonometric Functions are partial inverse Functions for trigonometric functions.
Now we will see the representation of inverse trigonometric functions:
Function        Inverse
Sin                arcsin
Cos              arccos
Tan               arctan
Sec               arcsec
Cosec          arccosec
Cot                arccot
Let’s talk about the relationship among the inverse trigonometric function.
For Complimentary angles:
Arccos y = âŠĽ / 2 – arcsin y;
Arccot y = âŠĽ / 2 – arctan y;
Arccsc y = âŠĽ / 2 – arcsec y;
Now we will see negative arguments:
Arcsin (-y) = - arcsin y;
Arccos (-y) = âŠĽ - arccos y;
Arctan (-y) = - arctan y;
Arccot (-y) = âŠĽ - arccot y;
Arcsec (-y) = âŠĽ - arcsec y;
Arccsc (-y) = - arccsc y;
The reciprocal arguments of inverse trig functions are;
Arccos (1 / y) = arcsec y;
Arcsin (1 / y) = arccsc y;
Arctan (1 / y) = ½ âŠĽ- arctan y = arccot y, if the value of ‘y’ is greater than zero;
Arctan (1 / y) = - ½ âŠĽ - arctan y = - âŠĽ+ arccot y, if the value of ‘y’ is less than zero;
Arccot (1 / y) = ½ âŠĽ- arccot y = arctan y, if the value of ‘y’ is greater than zero;
Arccot (1 / y) = - 3 / 2 âŠĽ - arccot y = âŠĽ+ 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 = arcsin

Arcsin y = 2arcsin y
1 + √ (y2 + 1),

Arccos y = arcsin
This function is satisfied if -1 ≤ y ≤ +1.

## The Inverse Cosine Function (arccos)

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## The Inverse Tangent Function (arctan)

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## The Inverse Sine Function (arcsin)

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or
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## The Inverse Secant Function (arcsec)

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## Inverse Trigonometric Functions Domain and Range

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## The Inverse Cosecant Function (arccsc)

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• ## Arctan Calculator

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