In two or more complete sentences, describe why the range of y = cos(x) is -1 ≤ y ≤ 1. Make sure to reference the unit circle in your description.
Mathematics · High School · Thu Feb 04 2021
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The range of y = cos(x) is -1 ≤ y ≤ 1 because the cosine of an angle represents the x-coordinate of a point on the unit circle—the circle with a radius of one unit centered at the origin of a coordinate plane. As the point moves around the unit circle for all possible angles x, its x-coordinate (the cosine value) varies from a maximum of 1, when the angle corresponds to a point on the far right of the circle (0 or 2π radians), to a minimum of -1, when the angle corresponds to a point on the far left of the circle (π radians). Since the x-coordinate of points on the unit circle cannot exceed the radius of the circle, the range of the cosine function must be constrained between -1 and 1.