To determine the equivalent rotation to [tex]\( R_{-200^{\circ}} \)[/tex], we will use the concept of angle normalization. The goal is to convert the given angle into an equivalent angle within the standard range of [tex]\([0^{\circ}, 360^{\circ})\)[/tex].
Here are the steps to solve this problem:
1. Normalize the Angle:
- Start with the original rotation angle, [tex]\(-200^{\circ}\)[/tex].
- To normalize this angle to fall within the [tex]\([0^{\circ}, 360^{\circ})\)[/tex] range, we need to add [tex]\(360^{\circ}\)[/tex] to it until it falls within this range.
2. Addition for Normalization:
- [tex]\(-200^{\circ} + 360^{\circ} = 160^{\circ}\)[/tex].
3. Interpret the Result:
- The equivalent angle in the standard range is [tex]\(160^{\circ}\)[/tex].
Given this result, we compare it to the provided options:
A. [tex]\( R_{160} \)[/tex]
B. [tex]\( R_{200} \)[/tex]
C. [tex]\( R_{560} \)[/tex]
D. [tex]\( R_{-160} \)[/tex]
The angle [tex]\(160^{\circ}\)[/tex] is listed as option A.
Thus, the rotation [tex]\( R_{-200^{\circ}} \)[/tex] is equivalent to:
[tex]\[ \boxed{R_{160}} \][/tex]
