Give Parameterizations for a Circle of Radius 3 in 3-Space $x = 4 + 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq 2 \pi$

question 20

Multiple Choice

Give parameterizations for a circle of radius 3 in 3-space perpendicular to the y-axis centered at (4, -2, 0) .

• A) \(x = 4 + 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq 2 \pi\)
• B) \(x = 4 + 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq \pi\)
• C) \(x = 4 + 3 \cos t , y = 3 \sin t , z = - 2 , \quad 0 \leq t \leq 2 \pi\)
• D) \(x = 4 + 3 \cos t , \quad z = 3 \sin t , \quad 0 \leq t \leq 2 \pi\)
• E) \(x = 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq 2 \pi\)

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Definitions:

Stroboscopic Motion

Perceived motion created by the rapid presentation of static images in sequence, similar to how motion pictures work.

Autokinetic Illusion

A visual phenomenon where a stationary point of light in a dark environment appears to move because of involuntary eye movements.

Texture Gradient

A depth cue based on the gradual reduction of detail that occurs in surfaces as they recede from the observer, used in perception to judge distances.

Brightness

The attribute of visual perception according to which an area appears to emit more or less light.