!************************************************************

! Param1

!

! Graphs the parametric equations (x(t),y(t)), which the

! user can vary.

! User can also sets values for tmin, tmax, and dt.

! If the picture goes off the screen, adjust the size of the

! window determined by the value of "s".

!Calculates the length of the curve

DEF x(t)

LET x = cos(t) !definition of x(t)

END DEF

DEF y(t)

LET y= sin(t) !definition of y(t)

END DEF

LET tmin = 0 ! min and max time interval

LET tmax = 2*pi ! for graphing function

LET dt = .001 ! time step

!sets the background variables for the program

LET s=4

LET xmin=-s !dimensions of the window

LET xmax =s

LET ymin =-s

LET ymax =s

LET length =0 !keeps track of the length

SET WINDOW xmin,xmax,ymin,ymax !produces window

PLOT LINES: 0,ymin;0,ymax !plots x,y axis

PLOT LINES: xmin,0;xmax,0

!plots the graph

FOR t = tmin to tmax step dt

PLOT x(t), y(t);

LET length_segment = sqr( (x(t+dt) - x(t))^2 + ( y(t+dt) - y(t))^2)

Let length = length + length_segment

NEXT t

PRINT "the approximate length of the curve with dt =", dt, "is", length

END