In two or more complete sentences, describe why the range of y = sin(x) is -1 ≤ y ≤ 1. Make sure to reference the unit circle in
your description.
2 answers:
The unit circle is a circle that is centered at the origin (0,0). The highest that it will go in terms of y is y = 1. The lowest y value is y = -1. So that's why y = sin(theta) is restricted in that manner. The sine function applies the ratio of the opposite site to the hypotenuse. For the unit circle, the hypotenuse is 1 since the radius is 1. Check out the image attachment for a reference drawing. The segment in red is the value of sin(theta) while the blue segment is the hypotenuse of 1. Dividing the red segment length over the blue segment length gets us sin(theta).
In short, the sine theta value is the height of the red segment point that sits on the unit circle. The highest that point goes is y = 1; the lowest it goes is y = -1.
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