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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 17 "INVERSE FUNCTIONS" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 31 "IN
VERSE TRIGONOMETRIC FUNCTIONS" }}{PARA 0 "" 0 "" {TEXT -1 17 "The sine
 function" }}{PARA 0 "" 0 "" {TEXT -1 51 "                            \+
          f(x) = sin x " }}{PARA 0 "" 0 "" {TEXT -1 78 "oscillates bet
ween  -1  and 1 as  x  varies over the extent of any interval of" }}
{PARA 0 "" 0 "" {TEXT -1 70 "length 2 Pi.  This means that the sine fu
nction does not have a unique" }}{PARA 0 "" 0 "" {TEXT -1 75 "inverse \+
function. Rather it has (infinitely) many inverses to (associated) " }
}{PARA 0 "" 0 "" {TEXT -1 81 "functions defined over intervals in whic
h the sine function is either increasing " }}{PARA 0 "" 0 "" {TEXT -1 
53 "or decreasing. The sine function is increasing on the" }}{PARA 0 "
" 0 "" {TEXT -1 79 "interval [-Pi/2,Pi/2] with range [-1,1].   In this
 case Maple V recognizes the " }}{PARA 0 "" 0 "" {TEXT -1 85 "inverse \+
to the sine function over the interval $[-Pi/2,Pi/2]$ as the arcsin fu
nction." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 18 "solve(y=sin(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'arcsi
nG6#%\"yG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Let us evaluate this function at  \+
x=-1." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "arcsin(-1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,$%#PiG#!\"\"\"\"#" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 86 "We plot the sine function,  the identity, and the arcsine
 function on the same graph. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot(\{sin(x),arcsin(x)\},x=-Pi/2..
Pi/2,y=-Pi/2..Pi/2);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
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" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Exercise 1. Ske
tch the inverse of  cos(x) by using the following Maple syntax:" }}}
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}}{PARA 0 "" 0 "" {TEXT -1 148 "Exercise 2. Find the inverse functions
 for each the following function AND graph the original function and t
he respective inverse function together." }}{PARA 0 "" 0 "" {TEXT -1 
16 "(a) f1(x) = 2^x;" }}{PARA 0 "" 0 "" {TEXT -1 60 "(b) f2(x) = log[5
](x)  (this is a log function with base 5];" }}{PARA 0 "" 0 "" {TEXT 
-1 26 "(c) f3(x) = 3*(x-4)^(1/3)." }}}}{MARK "5 0 0" 0 }{VIEWOPTS 1 1 
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