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12M02

Inverse Trigonometric Functions

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Introduction

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Inverse Trigonometric Functions

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Revision

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Trigonometric Functions

Domain

Range

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Trigonometric Functions

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

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Quadrant I

Quadrant II

Quadrant III

Quadrant IV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Recall Test

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Pause the video

(Time Duration : 2 Minutes)

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12M02.1

Graphical View of Inverse Trigonometric Functions

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12M02.1 – Graphical View of Inverse Trigonometric Functions (ITF)

Learning Objectives

Horizontal Line Test

Domain Restriction

Principal Value Branch

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12M02.1

CV 1

Graphical Method to Identify

Inverse Functions

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Injective

Surjective

Invertible Function

One – One Mapping

Onto Function

Bijective

 

 

 

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Not Invertible

Not Invertible

Not Invertible

Invertible

 

 

 

 

Many One Into

Many One Into

Many One Onto

One - One Onto

Horizontal Line Test

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Steps to find an Inverse Function

 

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Steps to find Inverse Trigonometric Functions

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NOTE

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12M02.1

CV 2

Domain Restriction

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12M02.1

CV 3

Principal Value Branch

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Principal Value Branch

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Sol.

(NCERT Ex – 2.1 Q – 1)

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Principal Value Branch

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12M02.1

PSV 1

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(NCERT Ex – 2.1 Q – 12)

Sol.

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Principal Value Branch

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Principal Value Branch

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Principal Value Branch

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Principal Value Branch

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12M02.1

PSV 2

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(NCERT Ex – 2.1 Q – 14)

Sol.

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12M02.1

ConcepTest

Ready for a challenge

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(NCERT Ex – 2.1 Q – 11)

 

 

 

 

Sol.

Pause the video

(Time Duration : 5 Minutes)

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Summary

Bijective Functions : Combination of One – One and Onto functions.

 

 

 

 

 

 

 

Domain and Range of Inverse Trigonometric Functions

Domain

Range

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Reference Questions

NCERT

:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

2, 3, 4, 5, 6, 7, 8, 9, 10, 13 (Ex. 2.1)

Work Book

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12M02.2

Properties of Inverse Trigonometric Functions

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12M02.2 – Properties of Inverse Trigonometric Functions (ITF)

Learning Objectives

 

 

 

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12M02.2

CV 1

Basic Properties of ITF

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Sol.

 

 

I

II

III

IV

 

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12M02.2

PSV 1

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Sol.

 

(NCERT Ex – 2.2 Q – 16)

 

 

 

 

I

II

III

IV

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12M02.2

CV 2

Transformation of ITF

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Sol.

 

 

 

 

 

 

 

 

 

 

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12M02.2

PSV 2

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Sol.

 

(NCERT Ex – 2.2 Q – 6)

 

 

 

 

 

 

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12M02.2

CV 3

Properties of ITF Part I

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Property I

 

 

 

 

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(Time Duration : 2 Minutes)

 

 

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II

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III

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IV

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II

IV

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II

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Property II

 

 

 

Pause the video

(Time Duration : 2 Minutes)

 

 

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Property III

 

 

 

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12M02.2

PSV 3

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Sol.

 

 

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12M02.2

CV 4

Properties of ITF Part II

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Property IV

 

 

 

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(Time Duration : 2 Minutes)

 

 

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Property V

 

 

 

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Sol.

 

 

 

 

 

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Property VI

 

 

 

 

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12M02.2

PSV 4

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Sol.

 

 

(NCERT Ex – 2.2 Q – 4)

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Properties of Inverse Trigonometric Functions

 

 

 

 

 

 

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12M02.2

ConcepTest

Ready for a challenge

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Sol.

 

 

(NCERT Ex – 2.2 Q – 15)

Pause the video

(Time Duration : 5 Minutes)

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Summary

Properties of Inverse Trigonometric Functions

 

 

 

 

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Summary

Properties of Inverse Trigonometric Functions

 

 

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Reference Questions

NCERT

:

12, 13, 14, 15, 16, 17, 18, 19, 20

1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20,

21 (Ex. 2.2)

Work Book

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