Find the exact value of each expression, if it is defined. Express your answer in radians. (If an answer is undefined,
(a) $\sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$
(b) $\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$
(c) $\tan ^{-1}(1)$

Step 1 ：The inverse sine function, or arcsine, is the inverse of the sine function. It returns the angle whose sine is a given number. We know that \( \sin(\frac{-\pi}{4}) = -\frac{\sqrt{2}}{2} \), so \( \sin ^{-1}\left(-\frac{\sqrt{2}}{2}\right) = -\frac{\pi}{4} \).

Step 2 ：The inverse cosine function, or arccosine, is the inverse of the cosine function. It returns the angle whose cosine is a given number. We know that \( \cos(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2} \), so \( \cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right) = \frac{3\pi}{4} \).

Step 3 ：The inverse tangent function, or arctangent, is the inverse of the tangent function. It returns the angle whose tangent is a given number. We know that \( \tan(\frac{\pi}{4}) = 1 \), so \( \tan ^{-1}(1) = \frac{\pi}{4} \).

Step 4 ：\(\boxed{-\frac{\pi}{4}}\), \(\boxed{\frac{3\pi}{4}}\), and \(\boxed{\frac{\pi}{4}}\) are the final answers.