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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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