Questions: What is the domain of the inverse sine function f(x)=cos^(-1)(x)?

Transcript text: What is the domain of the inverse sine function $f(x)=\cos ^{-1}(x)$ ?

Solution

Solution Steps

Step 1: Understand the Function

The function given is $ f(x) = \cos^{-1}(x) $, which is the inverse cosine function. The inverse cosine function returns the angle whose cosine is $ x $.

Step 2: Determine the Range of the Cosine Function

The cosine function, $ \cos(\theta) $, has a range of $[-1, 1]$. This means that the output of the cosine function is always between $-1$ and $1$.

Step 3: Identify the Domain of the Inverse Cosine Function

Since the inverse cosine function $ \cos^{-1}(x) $ is the inverse of the cosine function, its domain is the range of the cosine function. Therefore, the domain of $ f(x) = \cos^{-1}(x) $ is $[-1, 1]$.

Final Answer

$\boxed{[-1, 1]}$

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