Question

A circle with a 1-unit radius is centered at the origin of a coordinate plane where the x and y axes range from negative 1 to 1. A ray that starts at the origin and intersects at point P is drawn within the portion of the circle that resides in the first quadrant. P(15/17, 8/17)

Point P on the unit circle is given. What is the sine of the angle formed by a terminal ray that intersects the unit circle at this point?

(1 point)
Responses

−8/17
negative Start Fraction 8 over 17 End Fraction

−15/17
negative Start Fraction 15 over 17 End Fraction

15/17
Start Fraction 15 over 17 End Fraction

8/17

Answer 1

In the context of the unit circle, the coordinates of the point \( P \) are \( (x, y) = \left(\frac{15}{17}, \frac{8}{17}\right) \).

The sine of the angle formed by the terminal ray that intersects the unit circle at point \( P \) is given by the y-coordinate of the point where the ray intersects the unit circle.

Thus, the sine of the angle is:

\[
\sin(\theta) = y = \frac{8}{17}
\]

So the correct response is:

\(\frac{8}{17}\)