Answer:
[tex]-3/\sqrt{58}[/tex]
Step-by-step explanation:
tan = opposite / adjacent
opposite side is the y-coordinate of a point on the terminal side
adjacent side is the x-coordinate of a point on the terminal side
if the terminal side is in the second quadrant (the top-left quadrant), a coordinate on the terminal side would have a negative x-coordinate and a positive y-coordinate
This being the case:
the opposite side (y) would be -3 and the adjacent side (x) would be 7
using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
[tex]7^2+(-3)^2=c^2[/tex]
The hypotenuse is c, so it equals [tex]\sqrt{58}[/tex]
sin = opposite / hypotenuse
so sin(theta) = [tex]-3/\sqrt{58}[/tex]
