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Inverse Trigonometric Functions

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Inverse Trigonometric Functions. The arcsin. y = arcsin(x) 1. sin(y) = x and. 2. - /2 y /2 ... 1. tan(y) = x, and. 2. - /2 x /2. The arcsec. y = arcsec(x) 1. ... – PowerPoint PPT presentation

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Title: Inverse Trigonometric Functions


1
Inverse Trigonometric Functions
2
The arcsin
  • y arcsin(x) ?
  • 1. sin(y) x and
  • 2. -?/2 ? y ? ?/2

3
The arccos
  • y arccos(x) ?
  • 1. cos(y) x, and
  • 2. 0 ? y ? ?

4
The arctan
  • y arctan(x) ?
  • 1. tan(y) x, and
  • 2. -?/2 lt x lt ?/2

5
The arcsec
  • y arcsec(x) ?
  • 1. sec(y) x, and
  • 2. 0 ? y lt ?/2, or
    ?/2 lt y ? ?.

6
Derivatives of the Inverse Trig Functions
7
Arcsin
  • arcsin(x)
  • 1/?(1-x2) -1 lt x lt 1

8
Arctan
  • arctan(x) 1/(1x2) -? lt x lt ?

9
Arcsec
  • arcsec(x) 1/?x??(x2 1)
    ?x? gt 1
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