A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( 5,12 )$ Find $\sin \theta$
A) $- \frac { 12 } { 13 }$
B) $- \frac { 5 } { 13 }$
C) $\frac { 12 } { 13 }$
D) $\frac { 5 } { 13 }$

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 (5,12), we can form a right triangle with legs of lengths 5 and 12, and the hypotenuse can be found using the Pythagorean theorem: $\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$. Therefore, $\sin \theta = \frac{opposite}{hypotenuse} = \frac{12}{13}$.

A Point on the Terminal Side of an Angle θ (5,12)( 5,12 )(5,12)

A Point on the Terminal Side of an Angle θ $( 5,12 )$