To find an angle [tex]\( A \)[/tex] that is coterminal with [tex]\(-790^\circ\)[/tex] and lies within the range [tex]\( 0^\circ \leq A < 360^\circ \)[/tex], follow these steps:
1. Understand Coterminal Angles:
Coterminal angles are angles that share the same terminal side but may differ by full rotations of [tex]\(360^\circ\)[/tex]. Therefore, to find an equivalent angle within [tex]\([0^\circ, 360^\circ)\)[/tex], we can repeatedly add or subtract [tex]\(360^\circ\)[/tex] until the angle falls within the desired range.
2. Start with the Given Angle:
The given angle is [tex]\(-790^\circ\)[/tex].
3. Adjust the Angle into the Desired Range:
Since the given angle is negative, we will need to add [tex]\(360^\circ\)[/tex] repeatedly until the angle is within the range [tex]\([0^\circ, 360^\circ)\)[/tex].
- Add [tex]\(360^\circ\)[/tex] to [tex]\(-790^\circ\)[/tex]:
[tex]\[ -790 + 360 = -430 \][/tex]
- Again, add [tex]\(360^\circ\)[/tex] to [tex]\(-430^\circ\)[/tex]:
[tex]\[ -430 + 360 = -70 \][/tex]
- One more time, add [tex]\(360^\circ\)[/tex] to [tex]\(-70^\circ\)[/tex]:
[tex]\[ -70 + 360 = 290 \][/tex]
4. Result:
The coterminal angle [tex]\( A \)[/tex] that lies within the range [tex]\( 0^\circ \leq A < 360^\circ \)[/tex] and is coterminal with [tex]\(-790^\circ\)[/tex] is [tex]\( 290^\circ \)[/tex].
Therefore, the answer is:
[tex]\[ 290 \][/tex]
