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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "Objective 1. We will expl
ore trigonometric functions of the form: a*sin(b*x), a*tan(b*x), and a
*sec(b*x)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 194 "Exercise 1: Graph the following functions:  f(x) = sec(x
), g(x)=(1/2)*sec(x) and h(x) =(1/2)*sec(2*x)  (ii) Think about how to
 sketch functions g   and   h  once the graph of  y = f(x) is given." 
}}{PARA 0 "" 0 "" {TEXT -1 10 "Solution: " }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "f:=x->sec(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "g:=x->(1/2)*sec(x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "h:=x->(1/2)*sec(2*x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "plot(\{
f(x),g(x),h(x)\},x=-2*Pi..2*Pi,y=-10..10);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 48 "Note: Can you identify which one is which above?" }}}
{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Objective 2. We will explo
re some inverse trigonometric functions." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "f:=x->sin(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "f1:=x->arcsin(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "plot(f(x),x=-2*Pi..2*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 
"Note if we pick proper domain for sin(x), then it will have an invers
e, we restrict the domain in [-Pi/2, Pi/2]." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 61 "plot(\{f(x),f1(x)\},x=-Pi/2..Pi/2,y=-1..1,scaling=
constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Exercise 2: (a) \+
What are the domains and ranges of sin(x) and arcsin(x) respectively?
" }}{PARA 0 "" 0 "" {TEXT -1 57 "(b) How do we find arcsin(1/2) arcsin
(sqrt(3)/2) by hand?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sin
(Pi-Pi/3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(Pi/3);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "arcsin(sqrt(3)/2);" }}}}
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