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In trigonometry, the sine function represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. In quadrants 1 and 2, the angle is measured from the positive x-axis in a counterclockwise direction. Since the opposite side is positive in these quadrants and the hypotenuse is always positive, the sine function is positive. This is because the sine function is defined as positive when the opposite side is positive relative to the hypotenuse.
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SteveSine is = to opposite side/hypotenuse,
using a triangle with sides of opposite ~ 1, adjacent ~ 1 and hypotenuse ~ root(2),
hypotenuse is always positive,
hypotenuse = root(adjacent.squared * opposite.squared)
if either is negative, squaring them brings it back to a positive
and as the opposite side is the rise from the base line ( 0 degrees through to 180 degrees) it is positive in both quadrants 1 and 2
in quadrant 1, sine= 1/root(2) which is positive
in quadrant 2, sine= 1/root(2) which is positive
in quadrant 3, sine= -1/root(2) which is negative
in quadrant 4, sine= -1/root(2) which is negative
so sine is positive in quadrants 1 and 2 and is negative in 3 and 4
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