hp40g+.book Page 14 Friday, December 9, 2005 1:03 AM

the circle C, M will move on a curve Γ. In this exercise we will study and plot Γ.

1. Let t ∉ [–π,π]and m be the point on C of affix

z= ei ⋅ t . Find the coordinates of M in terms of t.

2.Compare x(–t) with x(t) and y(–t) with y(t).

3.Compute x′(t) and find the variations of x over [0, π].

4.Repeat step 3 for y.

5.Show the variations of x and y in the same table.

6.Put the points of Γ corresponding to t = 0, π/3, 2π/3 and π, and draw the tangent to Γ at these points.

Part 1

First go to CAS MODES

 

 

 

screen and make t the VX

 

 

 

variable. To do this, press

 

 

 

 

to open the Equation

 

 

 

Writer, and then press

 

 

 

 

 

. This opens

 

 

 

CAS

MODES screen. Press

and delete the current

 

variable. Type

T and press

.

 

Now enter the expression

 

 

 

1

2

– z and press

 

 

 

-- ⋅ z

 

 

 

 

2

 

it.

 

 

 

to select

 

 

 

Now invoke the SUBST

 

 

 

 

 

 

 

 

 

command from the

 

 

 

menu. Because the

 

 

 

expression was

 

 

 

highlighted, the SUBST

 

 

 

command is automatically

 

 

 

applied to it.

 

 

 

Note that the cursor is

 

 

 

 

 

 

positioned in the second

 

 

 

parameter. Since we know

 

 

 

that

z = ei ⋅ t , we can

 

 

 

enter this as the second

 

 

 

parameter.

 

 

16-14

 

 

Step-by-Step Examples