how to perform rotation matrix on ti 84 plus ce

Everly

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12-01-2025

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The TI-84 Plus CE calculator doesn't directly support matrix rotation in a single function. However, you can perform matrix rotation by utilizing its matrix operations and understanding the underlying mathematics. This article will guide you through the process.

Understanding Rotation Matrices

Before diving into the calculator steps, let's briefly review rotation matrices. A rotation matrix transforms a vector (or a set of points represented as vectors) by rotating it by a specified angle θ (theta) around the origin. The standard rotation matrices are:

• Rotation about the x-axis: This matrix rotates a point counter-clockwise around the x-axis.

Rx(θ) =  [[1,     0,     0],
         [0, cos(θ), -sin(θ)],
         [0, sin(θ),  cos(θ)]]

• Rotation about the y-axis: This matrix rotates a point counter-clockwise around the y-axis.

Ry(θ) =  [[cos(θ), 0, sin(θ)],
         [    0, 1,     0],
         [-sin(θ), 0, cos(θ)]]

• Rotation about the z-axis: This matrix rotates a point counter-clockwise around the z-axis.

Rz(θ) =  [[cos(θ), -sin(θ), 0],
         [sin(θ),  cos(θ), 0],
         [    0,      0, 1]]

Steps to Perform Rotation on your TI-84 Plus CE

These steps assume you have a point or set of points you want to rotate and an angle of rotation. Let's illustrate with a rotation about the z-axis.

1. Enter the Point(s) as a Matrix:

• Press [2nd][x⁻¹] (MATRIX)
• Go to EDIT and select a matrix (e.g., [A]).
• Define the dimensions of your matrix. If you have a single point (x, y), create a 2x1 matrix. For multiple points, create a 2xn matrix where 'n' is the number of points. Enter the x-coordinates in the first row and y-coordinates in the second.

2. Create the Rotation Matrix:

• Go back to the MATRIX menu ([2nd][x⁻¹]).

• Go to EDIT and select a different matrix (e.g., [B]).

• Set the dimensions of this matrix to 2x2.

• Enter the rotation matrix elements based on the chosen axis and angle. For a z-axis rotation with angle θ:

  [B] = [[cos(θ), -sin(θ)], [sin(θ), cos(θ)]]

  Remember to use the calculator's cos and sin functions. Make sure your calculator is in radian mode (Press MODE, select RADIAN).

3. Perform Matrix Multiplication:

• Press [2nd][x⁻¹] (MATRIX)
• Select the matrix you used for your points ([A]).
• Press [x] (multiplication).
• Press [2nd][x⁻¹] (MATRIX) again.
• Select the rotation matrix ([B]).
• Press [ENTER].

The resulting matrix will contain the rotated coordinates of your points.

Example: Rotating (2, 3) by 45 degrees counter-clockwise around the z-axis:

1. Matrix [A]: A 2x1 matrix containing [[2],[3]]
2. Matrix [B]: A 2x2 matrix: [[cos(45°), -sin(45°)],[sin(45°), cos(45°)]] (Remember to use radians!) This simplifies to approximately [[0.707, -0.707],[0.707, 0.707]]
3. Result: [A]*[B] will give you the rotated coordinates.

Handling 3D Rotations

For 3D rotations, you'll need 3x3 matrices for both your points and the rotation matrix. The process remains the same: define your points, create the appropriate 3x3 rotation matrix (using Rx, Ry, or Rz), and then perform matrix multiplication. Remember that for sequences of rotations, you must multiply the matrices in the correct order (matrix multiplication is not commutative).

Limitations

The TI-84 Plus CE has memory limitations. Large matrices might cause errors. Always double-check your matrix entries to avoid calculation mistakes.

This method requires a good understanding of linear algebra and rotation matrices. It's not a direct "rotation" function, but rather a way to utilize the calculator's matrix capabilities to achieve the desired rotation.