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) $\quad \sin \theta = - \frac { 17 } { 8 }$

Question

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) $\quad \sin \theta = - \frac { 17 } { 8 }$

Quizplus · Accepted Answer

We can use the formula $\sin 	heta = \frac{y}{r}$, where $y$ is the $y$-coordinate of the point $(x,y)$ on the terminal side of the angle, and $r$ is the distance from the origin to that point. Using the Pythagorean theorem, we find that the distance from $( - 8 , - 15 )$ to the origin is $\sqrt{8^2 + 15^2} = 17$. Therefore, $\sin 	heta = \frac{-15}{17}$, and the answer is $\boxed{	extbf{(C)}}$.

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