**Title: inverse-trigonometric-functions-by-sadiq-hussain** ** 1** (No Transcript)

** 2** CONCEPT INVERSE TRIGONOMETRIC FUNCTIONS Presentation on concept Delivery

By Mr SADIQ HUSSAIN Fazaia Inter College, Shaheen Camp, Peshawar ** 3** PRIOR KNOWLEDGE

Trigonometric functions Ordered pairs One-to-one function What is the horizontal line test? Domain and range of y sinx ** 4** THE AIM

To teach the student The Inverse sine Function ** 5** INTRODUCTION

Some questions will be asked to check if the students know What is real valued function? What is the inverse of yf(x)? What is the relation between f(x) and f-1(x)? What are the values of the following trigonometric ratio sin0, sin?/6, sin?/3, sin?/2 etc Example The following examples will be shown the class ** 6** INTRODUCTIONcontd

Q. Student will be asked to find f-1(x)? Good Q. Is f-1 again a function? A. Yes Q. What are the reasons? A. Because one-to-one correspondence between domain and range in f-1(x) is established. ** 7** INTRODUCTIONcontd

Q. Another relation f1 ( 0 , 1 ) ( -1 , 0 ) will be given to the class then student will be asked to interchanged the ordered pairs A. f2 ( 1 , 0 ) ( 0 , -1 ) Q. Student will be asked to depict these two relations f1 f2 on the graph paper? A. A graph will be shown Q. Student what you have noted from the graph of f1 and f2? ** 8** INTRODUCTIONcontd

A. Graph of f1 and f2 are reflection images of each other over the line yx Q. So, what should be the relation between f1 and f2? A. f2 is an inverse of f1. Very well students Here, teacher will clear as components of the order pairs of a 1-1 function are interchanged for its inverse function. ** 9** THE LESSON AIM

Now the aim of the lesson will be announced, Student today we will study the concept of The Inverse sine Function. ** 10** THE TOPIC

Topic The Inverse sine Function will be written on the board as centre heading THE INVERSE SINE FUNCTION ysin-1(x) ** 11** DEVELOPMENT

Concept ysin-1(x). Iff xsiny DLO The student will understand the concept of ysin-1(x) To find the angle y whose sine is x i.e xsiny ** 12** DEVELOPMENT contd

The Student will be asked to complete the given table f1 with respective sine f1 Expected Ans x -?/2 -?/3 -?/6 0 ?/6 ?/3 ?/2 y - - - - - - -

** 13** DEVELOPMENT contd

A graph will be shown to the class Q. Student will be asked to identify the graph f1, is it 1-1 function? A. No Q. What are the reasons? A. Because horizontal line cut the graph at many points. Good ** 14** DEVELOPMENT contd

Q. Student will be asked identify the graph whose horizontal line cut its only once? A. Only from Q. This part of the graph will be shown to the class? ** 15** DEVELOPMENT contd

Q. The student will be asked to interchange the ordered pairs of f1? Q. The student will be asked to depict these ordered pairs on the graph. A. A graph will be shown to the students

** 16** DEVELOPMENT contd

Q. The student will be asked that what conclusion you have drawn from the graph f1 and f2? A. f2 is the reflection of f1. A2. Opposite to sinx. ** 17** DEVELOPMENT contd

Very well, this is known as y sin-1x ** 18** DEVELOPMENT contd

Q. Student will be asked to find the value of sin-1(1)? Solution as a model will be done? A. Student, we have to find the angle whose sine is 1 let that angle be y, then ** 19** DEVELOPMENT contd

Q. Student will be asked to find (i) (ii) (iii) ** 20** LESSON SUMMARY

y sin-1x or arc sinx y sin-1x iff xsiny, where Domain of sin-1(x) is Range of sin-1x is The graph of sin-1x Combine graph of sin-1x and sin x ** 21** LESSON SUMMARYcontd

If x is ive, sin-1x will lie in If x is ive, sin-1x will lie in Caution sin-1x Find sin-1(1) ** 22** RECAPITULATION

An oral recap will be carried out in about three minutes which will cover the following points Today we have discussed the inverse sine function We have understood the domain of sin-1(x) Also, we have learnt the graph of sin-1(x) The student will be asked Was there anything you didnt comprehend well? Anything you would like to ask? ** 23** CONSOLIDATION

What do you meant by the inverse sine function? (Knowledge) What is the domain of ysin-1(x)? (Knowledge) What is the range of ysin-1(x)? (Knowledge) What is the difference b/w the graph of sinx and sin-1x? (Analysis) Find sin-1(-1)? (Application) Find sinsin-1(-1)? (Synthesis) ** 24** Homework

Q.1 Evaluate without using calculator. (i) (ii) (iii) ** 25** CONCLUSION

Today we have discussed the procedure of finding the inverse sine function i.e ysin-1(x). Next time we will discuss the inverse of cosine function. ** 26**THANK YOU