The positive x-axis passes through the 1st and 4th quadrants.
The line #y = 3x# increases from left to right because the slope is positive, so it passes through the 1st and 3rd quadrants.
Therefore, #theta# drawn in standard position will be an acute angle in the first quadrant.
We now find a point in the first quadrant on which the line #y = 3x# passes through. The simplest point with integral coordinates is #(1, 3)#.
If we were to draw a triangle, the side opposite #theta# would have measure #3# and the side adjacent #theta# would have measure #1#. By Pythagorean Theorem:
#(3)^2 + (1)^2 = h^2#
#10 = h^2#
#h = +-sqrt(10)#
But since we're talking about the hypotenuse, #h>0#. Therefore, #sintheta = "opposite"/"hypotenuse" = 3/sqrt(10) = (3sqrt(10))/10#.
Hopefully this helps!
