Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To solve the problem of determining the relationship between angle [tex]\(x\)[/tex] and angle [tex]\(y\)[/tex] when [tex]\(x\)[/tex] is coterminal with [tex]\(y\)[/tex] and the measure of angle [tex]\(x\)[/tex] is greater than angle [tex]\(y\)[/tex], let's first understand what it means for two angles to be coterminal.
1. Definition of Coterminal Angles:
- Two angles are said to be coterminal if they share the same terminal side. This means that they can differ by a full revolution (or multiple full revolutions) around the circle.
- A full revolution in degrees is 360°.
2. Mathematical Expression:
- Given an angle [tex]\(y\)[/tex], any angle [tex]\(x\)[/tex] that is coterminal with [tex]\(y\)[/tex] can be expressed as:
[tex]\[ x = y + 360k \][/tex]
where [tex]\(k\)[/tex] is an integer. This equation means that angle [tex]\(x\)[/tex] is obtained by adding or subtracting multiples of 360° to/from angle [tex]\(y\)[/tex].
3. Considering [tex]\(x > y\)[/tex]:
- Since it is given that the measure of angle [tex]\(x\)[/tex] is greater than the measure of angle [tex]\(y\)[/tex], we need to add multiples of 360° to [tex]\(y\)[/tex].
- Therefore, [tex]\(k\)[/tex] must be a positive integer so that when we add [tex]\(360k\)[/tex] to [tex]\(y\)[/tex], the resultant angle [tex]\(x\)[/tex] is greater than [tex]\(y\)[/tex].
4. Possible Statements Analysis:
- [tex]\(x = y - 180n\)[/tex] for any positive integer [tex]\(n\)[/tex]: This would not necessarily produce a coterminal angle because subtracting 180° does not yield a full circle equivalent.
- [tex]\(x = y - 380n\)[/tex] for any integer [tex]\(n\)[/tex]: This incorrect because 380° is not a full revolution and subtracting it does not ensure coterminal angles.
- [tex]\(x = y + 360n\)[/tex] for any positive integer [tex]\(n\)[/tex]: This is correct because adding 360° (or multiples of it) maintains the coterminal property and makes [tex]\(x\)[/tex] greater than [tex]\(y\)[/tex].
- [tex]\(x = y + 180n\)[/tex] for any integer [tex]\(n\)[/tex]: Adding 180° can sometimes produce an angle not necessarily coterminal because 180° is not a full revolution.
Hence, the correct statement regarding the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] is:
[tex]\[ x = y + 360n, \text{for any positive integer } n. \][/tex]
1. Definition of Coterminal Angles:
- Two angles are said to be coterminal if they share the same terminal side. This means that they can differ by a full revolution (or multiple full revolutions) around the circle.
- A full revolution in degrees is 360°.
2. Mathematical Expression:
- Given an angle [tex]\(y\)[/tex], any angle [tex]\(x\)[/tex] that is coterminal with [tex]\(y\)[/tex] can be expressed as:
[tex]\[ x = y + 360k \][/tex]
where [tex]\(k\)[/tex] is an integer. This equation means that angle [tex]\(x\)[/tex] is obtained by adding or subtracting multiples of 360° to/from angle [tex]\(y\)[/tex].
3. Considering [tex]\(x > y\)[/tex]:
- Since it is given that the measure of angle [tex]\(x\)[/tex] is greater than the measure of angle [tex]\(y\)[/tex], we need to add multiples of 360° to [tex]\(y\)[/tex].
- Therefore, [tex]\(k\)[/tex] must be a positive integer so that when we add [tex]\(360k\)[/tex] to [tex]\(y\)[/tex], the resultant angle [tex]\(x\)[/tex] is greater than [tex]\(y\)[/tex].
4. Possible Statements Analysis:
- [tex]\(x = y - 180n\)[/tex] for any positive integer [tex]\(n\)[/tex]: This would not necessarily produce a coterminal angle because subtracting 180° does not yield a full circle equivalent.
- [tex]\(x = y - 380n\)[/tex] for any integer [tex]\(n\)[/tex]: This incorrect because 380° is not a full revolution and subtracting it does not ensure coterminal angles.
- [tex]\(x = y + 360n\)[/tex] for any positive integer [tex]\(n\)[/tex]: This is correct because adding 360° (or multiples of it) maintains the coterminal property and makes [tex]\(x\)[/tex] greater than [tex]\(y\)[/tex].
- [tex]\(x = y + 180n\)[/tex] for any integer [tex]\(n\)[/tex]: Adding 180° can sometimes produce an angle not necessarily coterminal because 180° is not a full revolution.
Hence, the correct statement regarding the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] is:
[tex]\[ x = y + 360n, \text{for any positive integer } n. \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
