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

Question

Quizplus · Accepted Answer

The sine of an angle in standard position with a point on its terminal side $(-3, -4)$ 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: $\sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$. Therefore, $\sin \theta = \frac{-4}{5}$.

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