I am confused about the Unit Circle explanation for the trigonometric ratios for angles greater than 90 degrees.
It seems that for the first (top right) quadrant, $\sin(\theta)$ is equivalent to the y-coordinate, because
- $\sin(\theta)$ = opposite / hypotenuse
- $\sin(\theta)$ = opposite [hypotenuse is 1]
- $\sin(\theta)$ = y-coordinate [length of opposite side is the y-coordinate]
then, as theta extends in counter-clockwise manner to the top left quadrant, it is assumed that $\sin(\theta)$ is the still the value of the y-coordinate.
From what I understand, the basis for this is that because $\sin(\theta)$ is equivalent to the y-coordinate in the first quadrant, this extends to all quadrants. But this does not make sense to me because the $\sin(\theta)$ = o/h equation was applicable in the first quadrant but not in the others.
It seems to me that there are two definitions for the sine function:
The relationship between the opposite side and the hypotenuse for an acute angle in a right-angled triangle
The y-coordinate of a point along the unit circle, with angle theta (counter-clockwise from the x-axis)
The co-existence of these two definitions is making it confusing for me as it is not clear to me how we can get from the first to the second.