https://file.aiquickdraw.com/mathbot/file/17280599074924eme7ckk.jpg

Let's analyze the given mathematical expression.

The problem is to evaluate:

\[
\cos^{-1}(1)
\]

This represents the **inverse cosine**, also known as **arccosine**, of 1. In simpler terms, we're trying to find the angle whose cosine is 1.

The cosine function is equal to 1 at an angle of \(0\) radians (or \(0^\circ\)). Therefore:

\[
\cos^{-1}(1) = 0
\]

So the correct answer is \(0\), not \(-1\). It appears that there is an error in the input shown in the image.

Would you like me to explain further why \(\cos^{-1}(1) = 0\)? 

### Related Questions:
1. What is the value of \(\cos^{-1}(-1)\)?
2. What is the range of values for \(\cos^{-1}(x)\)?
3. How do you solve \(\sin^{-1}(1)\) without a calculator?
4. What is the domain of the function \(\cos^{-1}(x)\)?
5. Can you explain the difference between \(\cos^{-1}(x)\) and \(\sec(x)\)?

**Tip:** Remember that the inverse trigonometric functions return angles, and their range is restricted to make them functions, ensuring a unique value for each input in the domain.

Evaluate cos^(-1)(1) = -1 without using a calculator.

Learn how to evaluate cos^(-1)(1) without using a calculator. This problem focuses on the arccosine function, explaining why cos^(-1)(1) equals 0 radians and not -1. Suitable for students in Grades 10-12 studying trigonometry and inverse functions.

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