## Saturday, January 9, 2021

### TI 84 Plus: Plotting Circular Arcs with Just Two Points

TI 84 Plus: Plotting Circular Arcs with Just Two Points

Introduction

Knowing two points (x0, y0) and (x1, y1), we can draw a circular arc between two points.  We are going to assume that the points form the diameter of the circle.  Therefore, either point forms the radius along with the line's midpoint.   The midpoint between the points, labeled (A,B) is:

A = (x0 + x1) / 2, B = (y0 + y1) / 2

R = √((A - x0)^2 + (B - y0)^2) = √((x1 - A)^2 + (y1 - B)^2)

Set the parametric equations as:

x = R * (cos(t) + A / R)

y = R * (sin(t) + B / R)

With t being the range of required angle measure (θ), we have to determine the start and end points for the range of values for t.  Since (A, B) may not be the origin, we must take it into account the midpoint in determining the angle points:

t0 = atan((B - y0) / (A - x0)) mod 2*π

t1 = atan((y1 - B) / (x1 - A)) mod 2*π

The program ARC2PTS for the TI-84 Plus makes use the complex number functions abs and angle to determine radius and the angles, respectively.

TI-84 Plus Program: ARC2PTS

"2020-12-20 EWS"

a+bi

Param

FnOff

Input "X0? ",J

Input "Y0? ",K

Input "X1? ",L

Input "Y1? ",M

(J+L)/2→A

(K+M)/2→B

angle((A-J)+i(B-K))→C

If C<0:C+2π→C

angle((A-L)+i(B-M))→D

If D<0:D+2π→D

abs((A-J)+i(B-K))→R

"R(cos(T)+A/R)"→X₁T

"R(sin(T)+B/R)"→Y₁T

Lbl 1

min(C,D)→Tmin

max(C,D)→Tmax

Goto 3

Lbl 2

max(C,D)→Tmin

min(C,D)+2π→Tmax

Goto 3

Lbl 3

π/64→Tstep

ZoomFit

ZSquare

Examples

Example 1

Points:  (1,3) and (5,9), top part of the circle

Example 2

Points:  (-5, -8) and (-1, -7), bottom part of the circle

Eddie

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