Find the sine of an angle in radians on the unit circle
Answer 1
Sophia Williams
To find the sine of an angle on the unit circle, we need to find the y-coordinate of the point where the terminal side of the angle intersects the unit circle.
Let’s consider the angle \( \frac{5\pi}{6} \).
First, we need to identify the reference angle, which is the acute angle formed with the x-axis. For \( \frac{5\pi}{6} \), the reference angle is \( \pi – \frac{5\pi}{6} = \frac{\pi}{6} \).
On the unit circle, the coordinates of the point corresponding to \( \frac{\pi}{6} \) are \( ( \frac{\sqrt{3}}{2}, \frac{1}{2} ) \).
Since \( \frac{5\pi}{6} \) is in the second quadrant, the sine value (y-coordinate) remains positive.
Therefore, the sine of \( \frac{5\pi}{6} \) is:
$ \sin \left( \frac{5\pi}{6} \right) = \frac{1}{2} $
Answer 2
Isabella Walker
To determine the sine of the angle ( frac{5pi}{6} ) on the unit circle, we start by identifying the reference angle.
The reference angle for ( frac{5pi}{6} ) is ( pi – frac{5pi}{6} = frac{pi}{6} ).
On the unit circle, the coordinates for ( frac{pi}{6} ) are ( ( frac{sqrt{3}}{2}, frac{1}{2} ) ).
Since ( frac{5pi}{6} ) lies in the second quadrant, the y-coordinate is positive.
Therefore, the sine of ( frac{5pi}{6} ) is:
$ sin left( frac{5pi}{6}
ight) = frac{1}{2} $
Answer 3
Thomas Walker
The sine of ( frac{5pi}{6} ) is the y-coordinate of the corresponding point on the unit circle.
The reference angle is ( frac{pi}{6} ), and the coordinates are ( ( frac{sqrt{3}}{2}, frac{1}{2} ) ).
Since ( frac{5pi}{6} ) is in the second quadrant, the y-coordinate is:
$ sin left( frac{5pi}{6}
ight) = frac{1}{2} $
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