Answer
$1^o$
Work Step by Step
RECALL:
An angle $\theta$, where $-360^o \lt \theta \lt 0$, is coterminal with:
$\theta+ 360^o$
Thus, the given angle is coterminal with:
$=-359^o + 360^o
\\=1^o$
$-359^o$ is coterminal with $1^o$.
$1^o$ is in Quadrant I so $-359^o$ is also in Quadrant I.
RECALL:
The following are the means on how to find the reference angle of an angle $\theta$ based on its position:
(1) Quadrant I: $\theta$ (itself)
(2) Quadrant II: $180^o-\theta$
(3) Quadrant III: $\theta - 180^o$
(4) Quadrant IV: $360^o-\theta$
Use formula (1) above to obtain:
reference angle of $-359^o$ = reference angle of $1^o$, which is $1^o$.
