The point $( - 3 , - 4 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$.

A) $\sin \theta = - \frac { 3 } { 5 }$

B) $\sin \theta = - \frac { 2 } { 3 }$

C) $\sin \theta = - \frac { 4 } { 5 }$

D) $\sin \theta = - \frac { 1 } { 4 }$

E) $\sin \theta = - \frac { 5 } { 3 }$

Question

The point $( - 3 , - 4 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$.

A) $\sin \theta = - \frac { 3 } { 5 }$

B) $\sin \theta = - \frac { 2 } { 3 }$

C) $\sin \theta = - \frac { 4 } { 5 }$

D) $\sin \theta = - \frac { 1 } { 4 }$

E) $\sin \theta = - \frac { 5 } { 3 }$

Quizplus · Accepted Answer

We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the point $( - 3 , - 4 )$ and the origin $(0,0)$. The hypotenuse is $\sqrt { ( - 3 ) ^ { 2 } + ( - 4 ) ^ { 2 } } = 5$. Since the point is in the third quadrant, the sine of the angle is negative. Therefore, $\sin \theta = \frac {-4}{5}=\boxed{-\frac{4}{5}}$.

The Point (−3,−4)( - 3 , - 4 )(−3,−4) Is on the Terminal Side of an Angle in Standard

The Point $( - 3 , - 4 )$ Is on the Terminal Side of an Angle in Standard