Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( - 5,12 )$; find $\sin \theta$
A) $- \frac { 5 } { 13 }$
B) $- \frac { 12 } { 13 }$
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 the 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, $\sin \theta = \frac{opposite}{hypotenuse} = \frac{12}{13}$.

Suppose That θ\thetaθ Is in Standard Position and the Given Point Is on Point

Suppose That $\theta$ Is in Standard Position and the Given Point Is on Point