Find all angles, $0^{\circ} \leq \theta< 360^{\circ}$, that satisfy the equation below, to the nearest 1oth of a degree.
\[
\sin (\theta)=-\frac{\sqrt{6}}{3}
\]

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Answer

\boxed{234.7^\circ, 305.3^\circ}

Steps

Step 1 ：Find the reference angle in the first quadrant: $\sin^{-1}\left(-\frac{\sqrt{6}}{3}\right) \approx 54.7^\circ$

Step 2 ：Find the corresponding angles in the third and fourth quadrants: $180^\circ + 54.7^\circ = 234.7^\circ$ and $360^\circ - 54.7^\circ = 305.3^\circ$

Step 3 ：\boxed{234.7^\circ, 305.3^\circ}

Find all angles, $0^{\circ} \leq \theta< 360^{\circ}$, that satisfy the equation below, to the nearest 1oth of a degree.\[\sin (\theta)=-\frac{\sqrt{6}}{3}\]

Answer

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Find all angles, $0^{\circ} \leq \theta< 360^{\circ}$, that satisfy the equation below, to the nearest 1oth of a degree.
\[
\sin (\theta)=-\frac{\sqrt{6}}{3}
\]