Question

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.

Answer 1

The range of cos(x) is -1 to 1 (with brackets if in interval notation as -1 and 1 can be included) is because the radius of the unit circle is also 1. If the range went past -1 or 1, the unit circle could not define those values, and would turn up as error or undefined. Now, if you replace a in y = acos(x) + b, the range would be different because you amplified the equation and thus the range and radius.

Explanation: