The point $( - 8 , - 15 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$.
A) $\sin \theta = - \frac { 8 } { 17 }$
B) $\sin \theta = - \frac { 9 } { 8 }$
C) $\sin \theta = - \frac { 15 } { 17 }$
D) $\sin \theta = - \frac { 2 } { 15 }$
E) $\sin \theta = - \frac { 17 } { 8 }$

Question

Quizplus · Accepted Answer

The sine of an angle in standard position, where the point $(-8, -15)$ lies on its terminal side, is given by the ratio of the y-coordinate to the hypotenuse of the right triangle formed with the origin. The hypotenuse can be found using the Pythagorean theorem: $\sqrt{(-8)^2 + (-15)^2} = \sqrt{64 + 225} = \sqrt{289} = 17$. Therefore, $\sin \theta = \frac{-15}{17}$.

The Point (−8,−15)( - 8 , - 15 )(−8,−15) Is on the Terminal Side of an Angle in Standard

The Point $( - 8 , - 15 )$ Is on the Terminal Side of an Angle in Standard