A review of the unit circle will help you to understand this. The amplitude (the maximum displacement of a particle that exhibits the basic sine function (y =sin(x) is 1). The coordinates of any point on the unit circle are(cosx, sinx). The radius of the unit circle is 1. That is why it is called the unit circle.
Draw a circle of radius r = 1 unit. Looking at the unit circle, start from the 0°, that is the x-axis, at radius 1 on the circumference of the unit circle, and move counter-clockwise. The reference angle is 0 and sin(0) =0 and the coordinates are (1,0). At 90°, (on the y-axis, sin(90) is 1 and the coordinates are (0,1). The reference angle is the smallest angle from the x-axis. Between 90 and 180, the reference angle is less than 90°, and the sine of such reference angle is less than the absolute value of 1. At 270°, the reference angle is 90 and sin(270) = sin(-90°) = −1 and the coordinates are (0,-1) When it gets to 360°, the reference angle is 0 and you will be at the starting point again. Therefore, Sin(360) Sin(0) = 0 and the coordinates are (1,0). Then, the cycle is repeated.
MICHAEL E.
I like your answer, because it is very simple to follow. However, I like to add a little more to it. Consider the coordinate grid, with the origin at (0,0). In the 1st and 2nd quadrants, the opposite side is always a positive y-coordinate and the hypotenuse is always positive. Therefore Opposite/hypotenuse will be positive and between 0 and 1. In the 3rd and 4th quadrants, the opposite side will be always be a negative y-coordinate, and since the hypotenuse is always positive, Opposite/hypotenuse will be negative and between -1 and 0. Thank you for sharing.
05/26/18