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inverse-trigonometric-functions-by-sadiq-hussain

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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
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