Coordinate transformations – HP 33s User Manual
Page 254
15–32
Mathematics Programs
Example 3:
Find the roots of the following quadratic polynomial:
x
2
+ x – 6 = 0
Keys:
(In RPN mode)
Display:
Description:
X
P
@
value
Starts the polynomial root finder;
prompts for order.
2
g
@
value
Stores 2 in F; prompts for B.
1
g
@
value
Stores 1 in B; prompts for A.
6
^g
%/
.)
Stores –6 in A; calculates the first
root.
g
%/
)
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.