Docstoc

inverse trig deriv notes

Document Sample
inverse trig deriv notes Powered By Docstoc
					AP Calculus
Inverse Trig Derivative Notes

y = sin –1 x or y = arcsin x  this statement wants to know what angle makes the answer =
x.     You can also write this   x = sin y.

y = sin –1 ½

However, the domain must be restricted for each trigonometric function to have an
inverse. The accepted way to restrict each follows:

                    domain             range
    y = sin-1x      [-1, 1]             
                                       2 , 2 
                                              

    y = cos-1x      [-1, 1]            [0, ]

    y = tan-1x      (-, )             
                                       , 
                                       2 2

    y = cot-1x      (-, )            [0, ]

    y = sec-1x      |x| > 1         [0, ] y      
                                                   2

                    |x| > 1           
                                     ,  y  0
    y = csc x  -1                    2 2


What quadrants should you use for each trig function?

sec-1 2 =                     tan-1 –1 =               sin 1
                                                                3
                                                                2
                                                                                
                                                                          csc 1  2  


You may need to build a triangle to solve:
                                                                                x
sin(tan-1 x) =                  cos(sin-1 x2) =                       tan(sec-1 2 )=
Derivatives of inverse trig functions:

             u
1. y = sin-1 a  Find y'                                      re-write as x =
                                                              build a triangle
                                                              differentiate implicitly
                                                              use the triangle to sub
                                                             out the 'trig of y' function




Or you can memorize the following:
          function                 derivative
                      u
       y = arcsin a
                                                                      NOTE: Which ones are
                      u
       y = arcos a                                                    negative? Are any similar?
                                                                                   
                      u
       y = arctan a

                      u
       y = arccot a

                      u
      y = arcsec a


                      u
      y = arccsc a

Ex) y = arccos (3x)             Ex) y = tan-1 (ex)                  Ex) y = sec-1 x2




Ex) y = sin-1 (¼ x)                            Ex) y = arcsec e2x



                                                                       Assign: 5-6: Worksheet

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:2
posted:1/15/2012
language:
pages:2