Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

An angle measuring [tex]\( 468n^\circ \)[/tex] is in standard position. For which value of [tex]\( n \)[/tex] will the terminal side fall on the [tex]\( x \)[/tex]-axis?

A. [tex]\( n = 4 \)[/tex]
B. [tex]\( n = 5 \)[/tex]
C. [tex]\( n = 6 \)[/tex]
D. [tex]\( n = 7 \)[/tex]

Sagot :

GinnyAnswer
To determine for which value of [tex]\( n \)[/tex] the terminal side of the angle [tex]\( 468n \)[/tex] degrees in standard position falls on the [tex]\( x \)[/tex]-axis, we need to find when the angle is either [tex]\( 0^{\circ} \)[/tex] or [tex]\( 180^{\circ} \)[/tex] after reducing the angle to be within 0 to 360 degrees.

Here are the steps to solve the problem:

1. Calculate [tex]\( 468n \)[/tex] for each given [tex]\( n \)[/tex]:

- For [tex]\( n = 4 \)[/tex], the angle is [tex]\( 468 \times 4 = 1872 \)[/tex] degrees.
- For [tex]\( n = 5 \)[/tex], the angle is [tex]\( 468 \times 5 = 2340 \)[/tex] degrees.
- For [tex]\( n = 6 \)[/tex], the angle is [tex]\( 468 \times 6 = 2808 \)[/tex] degrees.
- For [tex]\( n = 7 \)[/tex], the angle is [tex]\( 468 \times 7 = 3276 \)[/tex] degrees.

2. Reduce each angle by taking modulo 360, which gives the angle within the standard 0 to 360 degrees range.

- For [tex]\( n = 4 \)[/tex], [tex]\( 1872 \mod 360 = 192 \)[/tex] degrees.
- For [tex]\( n = 5 \)[/tex], [tex]\( 2340 \mod 360 = 180 \)[/tex] degrees.
- For [tex]\( n = 6 \)[/tex], [tex]\( 2808 \mod 360 = 288 \)[/tex] degrees.
- For [tex]\( n = 7 \)[/tex], [tex]\( 3276 \mod 360 = 36 \)[/tex] degrees.

3. Check which angle lies on the [tex]\( x \)[/tex]-axis.

For an angle to fall on the [tex]\( x \)[/tex]-axis, it must be either [tex]\( 0^{\circ} \)[/tex] or [tex]\( 180^{\circ} \)[/tex].

- For [tex]\( n = 4 \)[/tex], the reduced angle is [tex]\( 192 \)[/tex], which is not on the [tex]\( x \)[/tex]-axis.
- For [tex]\( n = 5 \)[/tex], the reduced angle is [tex]\( 180 \)[/tex], which lies on the [tex]\( x \)[/tex]-axis.
- For [tex]\( n = 6 \)[/tex], the reduced angle is [tex]\( 288 \)[/tex], which is not on the [tex]\( x \)[/tex]-axis.
- For [tex]\( n = 7 \)[/tex], the reduced angle is [tex]\( 36 \)[/tex], which is not on the [tex]\( x \)[/tex]-axis.

Therefore, the value of [tex]\( n \)[/tex] for which the angle [tex]\( 468n \)[/tex] degrees falls on the [tex]\( x \)[/tex]-axis is [tex]\( n = 5 \)[/tex].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.