HP 33S - Coordinate Transformations

15–32 Mathematics Programs
File name 33s-E-Manual-1008-Publication(1st).doc Page : 386
Printed Date : 2003/10/8 Size : 13.7 x 21.2 cm
Example 3:
Find the roots of the following quadratic polynomial:
x
2
+ x – 6 = 0
Keys:
(In RPN mode)
Display: Description:
t
P

value

Starts the polynomial root finder;
prompts for order.
2
¥

value

Stores 2 its F; prompts for B.
1
¥

value

Stores 1 its B; prompts for A.
6
z¥


Stores –6 its A; calculates the first
root.
¥


Calculates the second root.
Coordinate Transformations
This program provides two–dimensional coordinate translation and rotation.
The following formulas are used to convert a point P from the Cartesian coordinate
pair (x, y) in the old system to the pair (u, v) in the new, translated, rotated system.
u = (x – m) cos
θ
+ (y – n) sin
θ
v = (y – n) cos
θ
–(x – m) sin
θ
The inverse transformation is accomplished with the formulas below.
x = u cos
θ
– v sin
θ
+ m
y = u sin
θ
+ v cos
θ
+ n
The HP 33s complex and polar–to–rectangular functions make these computations
straightforward.