inverse-trigonometric-functions-by-sadiq-hussain

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CONCEPT INVERSE TRIGONOMETRIC FUNCTIONS
Presentation on concept Delivery

• By
• Mr SADIQ HUSSAIN
• Fazaia Inter College, Shaheen Camp, Peshawar

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PRIOR KNOWLEDGE

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

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THE AIM

• To teach the student The Inverse sine Function

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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

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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.

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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?

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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.

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THE LESSON AIM

• Now the aim of the lesson will be announced,
  Student today we will study the concept of The
  Inverse sine Function.

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THE TOPIC

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

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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

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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 - - - - - - -
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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

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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?

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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
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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.

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DEVELOPMENT contd

• Very well, this is known as y sin-1x

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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

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DEVELOPMENT contd

• Q. Student will be asked to find
• (i)
• (ii)
• (iii)

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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

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LESSON SUMMARYcontd

1. If x is ive, sin-1x will lie in
2. If x is ive, sin-1x will lie in
3. Caution sin-1x
4. Find sin-1(1)

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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?

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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)

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Homework

• Q.1 Evaluate without using calculator.
• (i)
• (ii)
• (iii)

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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.

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• THANK YOU