Inverse Trigonometric Functions

  Principal Values

-p/2 < y < pi/2   0 < y < p
      y = arcsin x    y = arccos x 
      y = arccsc x    y = arcsec x
      y =arctan x    y = arccot x

Examples

  1. Arcsin 1 = 90o or p/2  (the angle whose sine is 1 = 90o)
  2. Cos-2\/3 = 30o or p/6 (the angle whose cos is \/3 is 30o)

    3.           2                                                              2
  3. Cos-1.3090 = 72o or 1.2567 radians (Press 2nd cos .3090 in the calculator)
  4. Arcsin .8007 = 53.197o or .9285 radians  (Press 2nd sin .8007 in the calculator)
  5. cos (Arccos \/2 ) = \/2  (Cos and Arccos are inverse functions so f(f-1(x)) = x)

    6.                     2        2
  6. Arcsin (sin (-2p/3)) = 2p/3 (Arcsin has a restricted range -p/2 < y < p/2.

    7. The problem becomes Arcsin (-\/3 ) = 2p/3)
  7. Find cos(Tan-1(2/3)) with your calculator.  Press cos(2nd tan (2/3))

    8.      Answer:  .8321
  8. Find cos(Tan-1(2/3)) without your calculator.

    9. Since tan 0 = 2/3, y = 2 and x = 3
    x2 + y2 = r2
    9 + 4 = r2
    13 = r2
    \/13 = r
    Thus, cos 0 =   3
                          \/13

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