Find all solutions of the equation in the interval $[0,2 \pi)$.
\[
\sin x=-\cos ^{2} x-1
\]
Write your answer in radians in terms of $\pi$. If there is more than one solution, separate them with commas.
\[
x=
\]

Answer

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Answer

Thus, the final answer is $\boxed{\text{No Solution}}$.

Steps

Step 1 ：Since $\sin x = \sqrt{1 - \cos^2 x}$, we get $-\sqrt{1 - \cos^2 x} = -\cos^2 x - 1$.

Step 2 ：Squaring both sides, we get $1 - \cos^2 x = \cos^4 x + 2\cos^2 x + 1$.

Step 3 ：Rearranging, we get $\cos^4 x + 2\cos^2 x - \cos^2 x + 2 = 0$, which simplifies to $\cos^4 x + \cos^2 x + 2 = 0$.

Step 4 ：This equation has no real solutions for $\cos x$, so there are no solutions for $x$ in the given interval.

Step 5 ：Thus, the final answer is $\boxed{\text{No Solution}}$.