Question 8 (5 points)

Find one positive and one negative angle coterminal with an angle of [tex]$166^{\circ}$[/tex].

A. [tex]526^{\circ}, -194^{\circ}[/tex]

B. [tex]516^{\circ}, -14^{\circ}[/tex]

C. [tex]526^{\circ}, -76^{\circ}[/tex]

D. [tex]256^{\circ}, -76^{\circ}[/tex]



Answer :

To find coterminal angles with a given angle, you can add or subtract multiples of [tex]\(360^\circ\)[/tex] to the given angle. Coterminal angles share the same initial and terminal sides.

Given an angle of [tex]\(166^\circ\)[/tex]:

1. Finding one positive coterminal angle:
- To find a positive coterminal angle, we add [tex]\(360^\circ\)[/tex] to the given angle:
[tex]\[ 166^\circ + 360^\circ = 526^\circ \][/tex]

2. Finding one negative coterminal angle:
- To find a negative coterminal angle, we subtract [tex]\(360^\circ\)[/tex] from the given angle:
[tex]\[ 166^\circ - 360^\circ = -194^\circ \][/tex]

Thus, one positive coterminal angle with [tex]\(166^\circ\)[/tex] is [tex]\(526^\circ\)[/tex] and one negative coterminal angle with [tex]\(166^\circ\)[/tex] is [tex]\(-194^\circ\)[/tex].

Among the given options:
- [tex]$526^{\circ},-194^{\circ}$[/tex]
- [tex]$516^{\circ},-14^{\circ}$[/tex]
- [tex]$526^{\circ},-76$[/tex]
- [tex]$256^{\circ},-76^{\circ}$[/tex]

The correct answer is:
[tex]\[ 526^{\circ}, -194^{\circ} \][/tex]