A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( 3 , - 2 )$ Find $\sin \theta$.
A) $- \frac { 2 \sqrt { 13 } } { 13 }$
B) $\frac { 3 \sqrt { 13 } } { 13 }$
C) $\frac { \sqrt { 13 } } { 3 }$
D) $- 2$

Question

Quizplus · Accepted Answer

The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Given a point (3, -2), we can form a right triangle with sides of length 3 and 2, and a hypotenuse that can be found using the Pythagorean theorem: $\sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13}$. Therefore, $\sin \theta = \frac{-2}{\sqrt{13}}$, which simplifies to $-\frac{2\sqrt{13}}{13}$ when rationalized.

A Point on the Terminal Side of Angle θ Is (3,−2)( 3 , - 2 )(3,−2)

A Point on the Terminal Side of Angle θ Is $( 3 , - 2 )$