Inverse Trigonometric Functions

posted on: 26 May, 2012 | updated on: 23 Aug, 2012

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 = ⊼ / 2 – arcsin y;
Arccot y = ⊼ / 2 – arctan y;
Arccsc y = ⊼ / 2 – arcsec y;
Now we will see 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;
The reciprocal arguments of inverse trig functions are;
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 = arcsin $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»y«/mi»«msqrt»«mrow»«mo»(«/mo»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«/msqrt»«/mfrac»«/math»$

Arcsin y = 2arcsin y
1 + √ (y² + 1),

Arccos y = arcsin $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msqrt»«mrow»«mo»(«/mo»«mn»1«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«msup»«mi»y«/mi»«mn»2«/mn»«/msup»«mo»)«/mo»«/mrow»«/msqrt»«mrow»«mn»1«/mn»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mi»y«/mi»«/mrow»«/mfrac»«/math»$
This function is satisfied if -1 ≤ y ≤ +1.

Topics Covered in Inverse Trigonometric Functions

The Inverse Cosine Function (arccos)

posted on: 20 Jun, 2012 | updated on: 21 Jun, 2012

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posted on: 21 Jun, 2012 | updated on: 22 Jun, 2012

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The Inverse Sine Function (arcsin)

posted on: 22 Jun, 2012 | updated on: 23 Jun, 2012

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The Inverse Secant Function (arcsec)

posted on: 27 Jul, 2012 | updated on: 28 Jul, 2012

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posted on: 30 Jul, 2012 | updated on: 23 Aug, 2012

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The Inverse Cosecant Function (arccsc)

posted on: 10 Jul, 2012 | updated on: 13 Jul, 2012

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