Finding the Sine of an Angle Using the Unit Circle
Answer 1
Abigail Nelson
Given a point on the unit circle corresponding to an angle of \( \frac{\pi}{6} \) (30°), determine the sine of the angle.
The unit circle has a radius of 1. For an angle of \( \frac{\pi}{6} \), the coordinates are:
$ \left( \cos \frac{\pi}{6}, \sin \frac{\pi}{6} \right) = \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) $
Therefore, the sine of \( \frac{\pi}{6} \) is:
$ \sin \frac{\pi}{6} = \frac{1}{2} $
Answer 2
Ella Lewis
Determine the sine of ( heta = 30^{circ} ) using the unit circle.
On the unit circle, the coordinates at ( 30^{circ} ) are found using the cosine and sine functions:
$ left( cos 30^{circ}, sin 30^{circ}
ight) = left( frac{sqrt{3}}{2}, frac{1}{2}
ight) $
Thus, the sine value is:
$ sin 30^{circ} = frac{1}{2} $
Answer 3
Lily Perez
What is the sine of 30°?
From the unit circle:
$ sin 30^{circ} = frac{1}{2} $
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