Lesson Plan Math Class 12 (Ch-2) For Mathematics Teacher

E- LESSON PLAN SUBJECT MATHEMATICS CLASS 10+2
Lesson Plan Class 12th Subject Mathematics for Mathematics Teacher. Effective way of Teaching Mathematics.Top planning by the teacher for effective teaching in the class.

E-LESSON PLAN MATHEMATICS
CLASS-XII | CHAPTER-2

INVERSE TRIGONOMETRIC FUNCTIONS (ITF)

NAME OF THE TEACHER				DINESH KUMAR
CLASS	10+2	CHAPTER	06	SUBJECT	MATHEMATICS
TOPIC	INVERSE TRIGONOMETRIC FUNCTIONS			DURATION : 10 Class Meetings

PRE- REQUISITE KNOWLEDGE:-

All formulas of trigonometry 10^th standard and 10+1 standard.

TEACHING AIDS:-

Green Board, Chalk, Duster, Charts, smart board, projector, laptop etc.

METHODOLOGY:- Lecture method

LEARNING OBJECTIVES:

All formulas of trigonometric functions.

Basic concepts related to the Inverse Trigonometric functions.

Domain and range of trigonometric functions.

Graphs of inverse trigonometric functions.

Properties of inverse trigonometric functions.

Some other important results without proof.

LEARNING OUTCOMES:

After studying this lesson students should know

all formulas of trigonometry
all formulas of inverse trigonometric functions.
Students should be able to apply the different formulas in the problems
students should understand properties of inverse trigonometric functions.

RESOURCES

NCERT Text Book,
NCERT Exemplar Book of mathematics,

Resource Material :

Worksheets , E-content, Basics and formulas from (cbsemathematics.com)

KEY WORDS

Inverse, Trigonometric Functions, Domain, Range, Quadrant, etc.

CONTENT OF THE TOPIC

LEARNING ACTIVITIES:

INTRODUCTORY ACTIVITY

Mathematics Activity No 05 Class XII

EXPERIENTIAL ACTIVITY

Mathematics Activity No 06 Class XII

ART INTEGRATED ACTIVITY

Mathematics Activity No 06 Class XII

PROCEDURE & EXPLANATION

Click Here for : Complete Explanation

Start the session by checking their previous knowledge, by asking the questions related to the trigonometry class 10^th and 10+1 . Now introduce the concept of trigonometry as follows.
Introduction
Here teacher will introduce the topic "inverse trigonometric functions" and make the discussion on all formulas of trigonometry class 10^th and 10+1
Simple meanings of Inverse of a Function
$y=sin^{-1}x\: \: \Rightarrow \: \: siny=x$
$f^{-1}of(x)\: \: \Rightarrow \: \: f^{-1}\left [ f(x) \right ]=x$
$sin^{-1}\:o \:\: sin\: x\Rightarrow \: \: sin^{-1}\left ( sin\:x \right )=x$
$sin^{2}x=(sinx)^{2} \: \: \: but \: \: \: sin^{-1}x\neq (sinx)^{-1}$
sinx is a function and sin^-1x is an angle
Domain and Range
Here teacher will explain the domain and range of trigonometric functions and relate that with their geometric explanation
Explanation of all basic concepts of inverse trigonometric functions, with simple problems on the topic.

Domain and range of inverse trigonometric functions and explanation with graphs.

Functions
Domain
(Value of x)
Range
(Value of y) Principal Value Branch
$y=sin^{-1}x$
[-1,1]
$\left [ -\frac{\pi }{2},\frac{\pi }{2} \right ]$
$y=cos^{-1}x$
[-1,1]
$[0,\pi ]$
$y=tan^{-1}x$
R
$\left (-\frac{\pi }{2},\frac{\pi }{2} \right )$
$y=cot^{-1}x$
R
$(0,\pi )$
$y=sec^{-1}x$
R-(-1,1)
$[0,\pi ]-\left \{ \frac{\pi }{2} \right \}$
$y=cosec^{-1}x$
R-(-1,1)
$\left [ -\frac{\pi }{2},\frac{\pi }{2} \right ]-\left \{ 0 \right \}$

Now teacher will introduce the formulas related to the properties of inverse trigonometric functions with detail.
Other Important Results

$sin^{-1}x+sin^{-1}y=sin^{-1}\left [ x\sqrt{1-y^{2}}+y\sqrt{1-x^{2}} \right ]$

$sin^{-1}x-sin^{-1}y=sin^{-1}\left [ x\sqrt{1-y^{2}}-y\sqrt{1-x^{2}} \right ]$

$cos^{-1}x+cos^{-1}y=cos^{-1}\left [ xy-\sqrt{1-x^{2}}\sqrt{1-y^{2}} \right ]$

$cos^{-1}x-cos^{-1}y=cos^{-1}\left [ xy+\sqrt{1-x^{2}}\sqrt{1-y^{2}} \right ]$

$tan^{-1}x+tan^{-1}y=tan^{-1}\left ( \frac{x+y}{1-xy} \right )$

$tan^{-1}x-tan^{-1}y=tan^{-1}\left ( \frac{x-y}{1+xy} \right )$

$tan^{-1}x+tan^{-1}y+tan^{-1}z=tan^{-1}\left ( \frac{x+y+z-xyz}{1-xy-yz-zx} \right )$

Now teacher will explain the method of solving the problems based on these properties by taking some problems. Teacher may assign some questions to the students to see their progress and guide them whenever they need.

STUDENTS DELIVERABLES:-

Review questions given by the teacher.

Students should make the presentation on the formulas of inverse trigonometric functions.
Solve NCERT problems with examples,
solve assignment given by the teacher.

EXTENDED LEARNING:-

Students can extend their learning in Mathematics through the RESOURCE CENTRE. Students can also find many interesting topics on mathematics at cbsemathematics.com

ASSESSMENT TECHNIQUES:-

Assignment sheet will be given as home work at the end of the topic.
Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
Re-test(s) will be conducted on the basis of the performance of the students in the test.

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