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]
