Question

A ray on the positive x-axis is rotated −450°
. What is the cosine of the angle formed by this rotation?

Answer 1

To find the cosine of the angle formed by rotating a ray on the positive x-axis by -450°, we can follow these steps:

1. **Determine the equivalent angle within the standard range**: Angles are often expressed in a range from 0° to 360°. To get an equivalent angle for -450°, we can add 360° until we find a positive angle:

\[
-450° + 360° = -90°
\]
\[
-90° + 360° = 270°
\]

So, -450° is equivalent to 270°.

2. **Find the cosine of the equivalent angle**: The cosine of 270° can be determined using the unit circle:

\[
\cos(270°) = 0
\]

Thus, the cosine of the angle formed by the rotation of the ray is \( \boxed{0} \).