Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Select all that are measures of angles that are coterminal with a [tex]\(-50^{\circ}\)[/tex] angle.

A. [tex]\(-770^{\circ}\)[/tex]
B. [tex]\(-530^{\circ}\)[/tex]
C. [tex]\(-410^{\circ}\)[/tex]
D. [tex]\(50^{\circ}\)[/tex]
E. [tex]\(310^{\circ}\)[/tex]
F. [tex]\(360^{\circ}\)[/tex]
G. [tex]\(410^{\circ}\)[/tex]
H. [tex]\(670^{\circ}\)[/tex]

Sagot :

GinnyAnswer
To determine which of the given angles are coterminal with [tex]\(-50^\circ\)[/tex], we need to understand what coterminal angles are. Angles are coterminal if they differ by multiples of [tex]\(360^\circ\)[/tex]. This means for an angle [tex]\(\theta\)[/tex], another angle [tex]\(\theta' \)[/tex] will be coterminal if [tex]\( \theta' - \theta \)[/tex] is a multiple of [tex]\(360^\circ\)[/tex].

Given the angle [tex]\(-50^\circ\)[/tex], we're looking for angles that satisfy:

[tex]\[ (\theta' + 50) = 360n \][/tex]

where [tex]\(n\)[/tex] is an integer.

Checking each angle:
1. [tex]\(-770^\circ\)[/tex] :
[tex]\[ -770 + 50 = -720 \][/tex]
[tex]\[ -720 \div 360 = -2 \][/tex]
So, [tex]\(-770^\circ\)[/tex] is coterminal with [tex]\(-50^\circ\)[/tex].

2. [tex]\(-530^\circ\)[/tex] :
[tex]\[ -530 + 50 = -480 \][/tex]
[tex]\[ -480 \div 360 = -4/3 \quad (\text{not an integer}) \][/tex]
So, [tex]\(-530^\circ\)[/tex] is not coterminal with [tex]\(-50^\circ\)[/tex].

3. [tex]\(-410^\circ\)[/tex] :
[tex]\[ -410 + 50 = -360 \][/tex]
[tex]\[ -360 \div 360 = -1 \][/tex]
So, [tex]\(-410^\circ\)[/tex] is coterminal with [tex]\(-50^\circ\)[/tex].

4. [tex]\(50^\circ\)[/tex] :
[tex]\[ 50 + 50 = 100 \][/tex]
[tex]\[ 100 \div 360 = 5/18 \quad (\text{not an integer}) \][/tex]
So, [tex]\(50^\circ\)[/tex] is not coterminal with [tex]\(-50^\circ\)[/tex].

5. [tex]\(310^\circ\)[/tex] :
[tex]\[ 310 + 50 = 360 \][/tex]
[tex]\[ 360 \div 360 = 1 \][/tex]
So, [tex]\(310^\circ\)[/tex] is coterminal with [tex]\(-50^\circ\)[/tex].

6. [tex]\(360^\circ\)[/tex] :
[tex]\[ 360 + 50 = 410 \][/tex]
[tex]\[ 410 \div 360 = 1.138 \quad (\text{not an integer}) \][/tex]
So, [tex]\(360^\circ\)[/tex] is not coterminal with [tex]\(-50^\circ\)[/tex].

7. [tex]\(410^\circ\)[/tex] :
[tex]\[ 410 + 50 = 460 \][/tex]
[tex]\[ 460 \div 360 = 1.278 \quad (\text{not an integer}) \][/tex]
So, [tex]\(410^\circ\)[/tex] is not coterminal with [tex]\(-50^\circ\)[/tex].

8. [tex]\(670^\circ\)[/tex] :
[tex]\[ 670 + 50 = 720 \][/tex]
[tex]\[ 720 \div 360 = 2 \][/tex]
So, [tex]\(670^\circ\)[/tex] is coterminal with [tex]\(-50^\circ\)[/tex].

The angles that are coterminal with [tex]\(-50^\circ\)[/tex] are:

[tex]\[ -770^\circ, -410^\circ, 310^\circ, 670^\circ \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. 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.