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Math12 lesson7
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Transcript

  • 1. INVERSE TRIGONOMETRIC FUNCTIONS
  • 2. DEFINITION: If is a one-to-one function with domain A and range B, then its inverse is the function with domain B and range A defined by
    For a function to have an inverse, it must be one-to-one. Since the trigonometric functions are not one-to-one, they do not have inverses. It is possible, however, to restrict the domains of the trigonometric functions in such a way that the resulting functions are one-to-one.
  • 3. Inverse trigonometric functions are defined as follows:
    y
    x
    o
    y = sinx
    y
    x
    y = sin-1 x
  • 4. y
    x
    o
    y = cosx
    y
    x
    y = cos-1 x
  • 5. y
    x
    o
    y = tanx
    y
    x
    y = tan-1 x
  • 6. y
    x
    o
    y = cotx
    y
    x
    y = cot-1 x
  • 7. y
    x
    o
    y = secx
    y
    x
    y = sec-1 x
  • 8. y
    x
    o
    y = cscx
    y
    x
    y = csc-1 x
  • 9. EXAMPLE:
    Find the exact values of the following:
  • 10.
  • 11.
  • 12. II. Solve for x:
  • 13. EXERCISES:
    Find the exact values of the following: