Question

Which inverse trigonometric function has a range of left bracket 0 comma pi right bracket?
(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 cosecant x
Image with alt text: y equals cosecant x

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

Answer 1

The inverse trigonometric function that has a range of \( (0, \pi) \) is:

**y = inverse cotangent x**

This function, denoted as \( y = \cot^{-1}(x) \), takes values from \( 0 \) to \( \pi \) (exclusive) as \( x \) varies.

The other functions listed have the following ranges:
- \( \text{inverse cosine} \): \( [0, \pi] \)
- \( \text{cosecant} \): not an inverse function in this context
- \( \text{inverse sine} \): \( [-\frac{\pi}{2}, \frac{\pi}{2}] \)

So the correct answer is **y = inverse cotangent x**.