Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ.
-$( - 20,48 ) ;$ 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 a point $(-20, 48)$, we can form a right triangle with legs of lengths 20 and 48 (ignoring signs for the moment), and the hypotenuse can be found using the Pythagorean theorem: $\sqrt{(-20)^2 + 48^2} = \sqrt{400 + 2304} = \sqrt{2704} = 52$. Thus, $\sin \theta = \frac{opposite}{hypotenuse} = \frac{48}{52} = \frac{12}{13}$. The positive value is correct because the point $(-20, 48)$ is in the second quadrant, where sine is positive.

Suppose That θ Is in Standard Position and the Given (−20,48);( - 20,48 ) ;(−20,48);

Suppose That θ Is in Standard Position and the Given $( - 20,48 ) ;$