Question

The graph of an inverse trigonometric function passes through the point left parenthesis 1 comma Start Fraction pi over 2 End Fraction right parenthesis. Which of the following could be the equation of the function?
(1 point)
Responses

y equals inverse cosine x
Image with alt text: y equals inverse cosine x

y equals inverse cotangent x
Image with alt text: y equals inverse cotangent x

y equals inverse sine x
Image with alt text: y equals inverse sine x

y equals inverse tangent x

Answer 1

To determine which inverse trigonometric function passes through the point \((1, \frac{\pi}{2})\), we need to evaluate each of the given functions at \(x = 1\) and see if any result in \(y = \frac{\pi}{2}\):

1. **\(y = \arccos(x)\)**:
- \(\arccos(1) = 0\)
- This does not equal \(\frac{\pi}{2}\).

2. **\(y = \arccot(x)\)**:
- \(\arccot(1) = \frac{\pi}{4}\)
- This does not equal \(\frac{\pi}{2}\).

3. **\(y = \arcsin(x)\)**:
- \(\arcsin(1) = \frac{\pi}{2}\)
- This equals \(\frac{\pi}{2}\).

4. **\(y = \arctan(x)\)**:
- \(\arctan(1) = \frac{\pi}{4}\)
- This does not equal \(\frac{\pi}{2}\).

Thus, the only function that passes through the point \((1, \frac{\pi}{2})\) is:

**\(y = \arcsin(x)\)**.