Get insightful responses to your questions quickly and easily on IDNLearn.com. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.
Sagot :
To find an equivalent rotation angle when given a negative rotation of [tex]\(-500^{\circ}\)[/tex], we first need to normalize this angle within the range [tex]\(0^{\circ}\)[/tex] to [tex]\(360^{\circ}\)[/tex].
Here's how we can do this step-by-step:
1. Understanding the Problem:
We need an equivalent angle to [tex]\(-500^{\circ}\)[/tex] that lies between [tex]\(0^{\circ}\)[/tex] and [tex]\(360^{\circ}\)[/tex].
2. Normalization Step:
Normalize the angle by using the modulo operation with [tex]\(360^{\circ}\)[/tex].
[tex]\[ \text{normalized\_angle} = -500 \mod 360 \][/tex]
3. Calculating the Normalized Angle:
The modulo operation essentially tells us the remainder when [tex]\(-500\)[/tex] is divided by [tex]\(360\)[/tex]. But given it's negative, it's useful to visualize the operation:
- Start from [tex]\(-500\)[/tex]
- Add [tex]\(360\)[/tex] repeatedly until the result is between [tex]\(0^{\circ}\)[/tex] and [tex]\(360^{\circ}\)[/tex].
[tex]\[ -500 + 360 = -140 \][/tex]
[tex]\[ -140 + 360 = 220 \][/tex]
So, the equivalent positive angle is [tex]\(220^{\circ}\)[/tex].
4. Final Equivalent Angle:
The angle [tex]\(220^{\circ}\)[/tex] is within the range [tex]\(0^{\circ}\)[/tex] to [tex]\(360^{\circ}\)[/tex], and it represents the same rotation about the origin as [tex]\(-500^{\circ}\)[/tex] but in the positive direction.
Therefore, the equivalent rotation about the origin for [tex]\(-500^{\circ}\)[/tex] is:
[tex]\[ \boxed{220^{\circ}} \][/tex]
Conclusion:
[tex]\[ \text{Option B. } R_{220} \][/tex]
Here's how we can do this step-by-step:
1. Understanding the Problem:
We need an equivalent angle to [tex]\(-500^{\circ}\)[/tex] that lies between [tex]\(0^{\circ}\)[/tex] and [tex]\(360^{\circ}\)[/tex].
2. Normalization Step:
Normalize the angle by using the modulo operation with [tex]\(360^{\circ}\)[/tex].
[tex]\[ \text{normalized\_angle} = -500 \mod 360 \][/tex]
3. Calculating the Normalized Angle:
The modulo operation essentially tells us the remainder when [tex]\(-500\)[/tex] is divided by [tex]\(360\)[/tex]. But given it's negative, it's useful to visualize the operation:
- Start from [tex]\(-500\)[/tex]
- Add [tex]\(360\)[/tex] repeatedly until the result is between [tex]\(0^{\circ}\)[/tex] and [tex]\(360^{\circ}\)[/tex].
[tex]\[ -500 + 360 = -140 \][/tex]
[tex]\[ -140 + 360 = 220 \][/tex]
So, the equivalent positive angle is [tex]\(220^{\circ}\)[/tex].
4. Final Equivalent Angle:
The angle [tex]\(220^{\circ}\)[/tex] is within the range [tex]\(0^{\circ}\)[/tex] to [tex]\(360^{\circ}\)[/tex], and it represents the same rotation about the origin as [tex]\(-500^{\circ}\)[/tex] but in the positive direction.
Therefore, the equivalent rotation about the origin for [tex]\(-500^{\circ}\)[/tex] is:
[tex]\[ \boxed{220^{\circ}} \][/tex]
Conclusion:
[tex]\[ \text{Option B. } R_{220} \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.