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

Here's what I get

Explanation:

The range is the spread of the y-values (minimum to maximum).

cos x = adjacent/hypotenuse

In terms of the unit circle,

"adjacent" = x

"hypotenuse" = 1, so

cos x = the x-coordinate

Let's evaluate cos x as we go around the unit circle.

`\begin{array}{rr}\mathbf{x/^(\circ)} & \mathbf{\cos x} \\0 & 1 \\90 &0 \\180 & -1 \\270 & 0 \\360 & 1 \\\end{array}`

The function y = cos x starts at 1, then decreases smoothly through 0 at 90° to -1 at 180°.

It then increases smoothly through 0 at 270° to 1 at 360°, and the cycle repeats.

The minimum value is -1.

The maximum value is 1

The range is −1 ≤ y ≤ 1.