$ ext{What does sin represent on the unit circle?}$
Answer 1
Charlotte Davis
On the unit circle, the sine of an angle represents the y-coordinate of the point on the unit circle that corresponds to that angle.
$\text{Given an angle } \theta, \text{the coordinates of the point P on the unit circle are } (\cos(\theta), \sin(\theta)).$
This means:
$\sin(\theta) = y.$
For example, if \(\theta = 30^\circ\):
$\sin(30^\circ) = \frac{1}{2}.$
Answer 2
Daniel Carter
On the unit circle, the sine function measures the vertical distance from the x-axis to the point where the terminal side of the angle intersects the circle.
$ ext{Consider an angle } heta ext{ in standard position. The coordinates of the point where the angle’s terminal side intersects the unit circle are } (cos( heta), sin( heta)).$
Thus:
$sin( heta) = ext{y-coordinate of the point}.$
For instance, if ( heta = 45^circ):
$sin(45^circ) = frac{sqrt{2}}{2}.$
Answer 3
Chloe Evans
On the unit circle, sine represents the y-coordinate of a point.
$ ext{Given } heta, ext{we find } P(cos( heta), sin( heta)).$
Therefore:
$sin( heta) = y.$
For ( heta = 90^circ):
$sin(90^circ) = 1.$
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