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2 cards from this section. Quick, good the night before a test.
What is the angle in degrees for a rotation that turns a point (1, 0) to (0, 1)?
Think about how many quarter turns are needed.
What are the sine and cosine values for a 0-degree rotation?
Values relate to the position on a unit circle.
What transformation does a rotation matrix facilitate?
Think about how we adjust angles and positions.
True or False: Rotations in 3D can happen about multiple axes.
Visualize a 3D object and how each axis affects its position.
A geometric object rotates 90 degrees about the y-axis followed by a 45-degree rotation about the z-axis. Determine the new coordinates of the point (2, 1, 1).
Use corresponding rotation matrices for each axis and apply them sequentially.
If a point (1, 1, 0) undergoes a consecutive rotation of 180 degrees about the z-axis and then a 90-degree rotation about the x-axis, what are the resulting coordinates?
Apply each rotation matrix in the order given.
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