Monday, August 13, 2012

Applications and Programming: Rotation of a Graph

Rotation of a Function - TI-84+

The following program rotates the function y1(x) at an angle θ. The angle θ is measured counterclockwise, with θ = 0 indicating due east (positive x direction).

Let the coordinates (x', y') be e new coordinates after rotating the original coordiante, (x, y) at an angle θ. Then (x', y') can be calculated by the following equations:

x' = x cos θ - y sin θ
y' = x sin θ + y cos θ

The rotated coordinates are compiled into two lists: one for x', and the other for y'. A stat plot is made of the resulting lists.

Steps (TI-84+):

1. Store Y1. Two ways to do this:
* Press Y=, then edit Y1, or
* Type the function in quotes and store it in the variable Y1.

2. Run ROTATEY1 (see below). The original Y1 is graphed along its rotated sibling.

Two screen shots of examples are shown below. Have fun,


Eddie

This blog is property of Edward Shore. © 2012



Program ROTATEY1 - TI-84+


: Func
: FnOff
: PlotsOff
: FnOn 1
: PlotsOn 1
: Radian
: Disp "TYPE ° FOR DEGREES"
: Input "θ:", θ
: Xmin → X
: {X cos( θ ) - Y1 sin(θ → L1
: {X sin( θ ) - Y1 cos(θ → L2
: 1→ C
: For(K,Xmin,Xmax - ΔX, ΔX)
: K + ΔX → X
: augment(L1, {X cos( θ ) - Y1 sin(θ → L1
: augment(L2, {X sin( θ ) - Y1 cos(θ → L2
: C + 1 → C
: ClrHome
: Output(1,1,"PROGRESS:
: Output(2,1,"round(100C/95,2
: End
: Plot(Scatter,L1,L2, square or marker of your choice
: DispGraph




1 comment:

  1. A graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges.Interpreting Graphs

    ReplyDelete

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