Question
Point P on the unit circle is given. P(15/17, 8/17). What is the sine of the angle
Answers
GPT-4o mini
Point \( P \) on the unit circle is given as \( P\left(\frac{15}{17}, \frac{8}{17}\right) \).
In the context of the unit circle, the coordinates of a point on the unit circle represent \( (\cos \theta, \sin \theta) \) for some angle \( \theta \). Here, the x-coordinate corresponds to \( \cos \theta \) and the y-coordinate corresponds to \( \sin \theta \).
From the coordinates of the point \( P \):
- \( \cos \theta = \frac{15}{17} \)
- \( \sin \theta = \frac{8}{17} \)
Thus, the sine of the angle \( \theta \) is:
\[
\sin \theta = \frac{8}{17}
\]
Therefore, the sine of the angle is \( \frac{8}{17} \).
In the context of the unit circle, the coordinates of a point on the unit circle represent \( (\cos \theta, \sin \theta) \) for some angle \( \theta \). Here, the x-coordinate corresponds to \( \cos \theta \) and the y-coordinate corresponds to \( \sin \theta \).
From the coordinates of the point \( P \):
- \( \cos \theta = \frac{15}{17} \)
- \( \sin \theta = \frac{8}{17} \)
Thus, the sine of the angle \( \theta \) is:
\[
\sin \theta = \frac{8}{17}
\]
Therefore, the sine of the angle is \( \frac{8}{17} \).