What does the $ sin $ function represent on the unit circle?
Answer 1
Chloe Evans
On the unit circle, the sine function $ \sin(\theta) $ represents the y-coordinate of a point on the circle corresponding to the angle $ \theta $ measured from the positive x-axis.
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Mathematically, if a point on the unit circle is given by $ (x, y) $, then for any angle $ \theta $, the coordinates can be expressed as:
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$ x = \cos(\theta) $
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$ y = \sin(\theta) $
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This implies that the sine of an angle is the vertical distance from the x-axis to the point on the circle.
Answer 2
Ava Martin
The $ sin( heta) $ function represents the y-coordinate of the corresponding point on the unit circle for a given angle $ heta $.
For a point $ (x, y) $ on the unit circle:
$ y = sin( heta) $
The value of $ sin( heta) $ is the length of the line segment from the origin to the point projected onto the y-axis.
Answer 3
Christopher Garcia
The $ sin( heta) $ function represents the y-coordinate of a point on the unit circle for angle $ heta $.
$ y = sin( heta) $
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