Use a sketch to find the exact value of $y$.
\[
y=\sin \left[\cos ^{-1}\left(-\frac{24}{25}\right)\right]
\]
\[
\sin \left[\cos ^{-1}\left(-\frac{24}{25}\right)\right]=
\]
(Simplify your answer, including any radicals. Use

Step 1 ：The problem is asking for the value of \(y\) where \(y=\sin \left[\cos ^{-1}\left(-\frac{24}{25}\right)\right]\). This is a composition of trigonometric functions.

Step 2 ：The inner function is \(\cos^{-1}\left(-\frac{24}{25}\right)\), which is the angle whose cosine is \(-\frac{24}{25}\).

Step 3 ：The outer function is \(\sin(x)\), which is the sine of the angle.

Step 4 ：We can use the Pythagorean identity \(\sin^2(x) + \cos^2(x) = 1\) to find the value of \(\sin(x)\) when we know \(\cos(x)\).

Step 5 ：In this case, we know that \(\cos(x) = -\frac{24}{25}\), so we can solve for \(\sin(x)\) using the Pythagorean identity.

Step 6 ：The value of \(\sin \left[\cos ^{-1}\left(-\frac{24}{25}\right)\right]\) is the same as the value of \(\sin(x)\) when \(\cos(x) = -\frac{24}{25}\). We found that \(\sin(x) = 0.28\) when \(\cos(x) = -\frac{24}{25}\). Therefore, the value of \(y\) is \(0.28\).

Step 7 ：Final Answer: The exact value of \(y\) is \(\boxed{0.28}\).