The given graph shows a curve that starts at (−1,π), passes through (0,2π), and ends at (1,0) — this is exactly the principal branch of y=cos−1x. The correct option is (C).
The key to identifying an inverse trigonometric graph lies in knowing the principal value branches — the restricted domains and ranges that make each inverse function one-to-one. For sin−1x, the range is [−2π,2π]; for cos−1x, it’s [0,π]; for tan−1x, it’s (−2π,2π). The graph given in the question (not shown here, but described in the options) has a starting point at x=−1, y=π, passes through (0,2π), and ends at (1,0). That immediately tells you the range is [0,π] and the domain is [−1,1] — the signature of cos−1x.
Let’s walk through the reasoning step by step.
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Eliminate the impossible options first.
Option (A) describes y=tanx, which is a trigonometric function, not its inverse. The question asks for the graph of the inverse, so (A) is out.
Option (B) describes y=sin−1x with range [−2π,2π]. Its graph starts at (−1,−2π) and ends at (1,2π), passing through (0,0). The given graph passes through (0,2π), not (0,0), so (B) is incorrect.
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Compare the two remaining options: (C) and (D).
Both claim the graph is y=cos−1x, with the same starting and ending points and the same point (0,2π). They are identical in description. This is a trick — the question likely expects you to notice that (C) and (D) are word-for-word the same. In such multiple-choice questions, if two options are identical, they cannot both be correct; the correct one is the one that matches the graph. Since the description fits cos−1x perfectly, the answer must be either (C) or (D). But because they are duplicates, the intended correct choice is (C) (often the first occurrence in such lists).
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Confirm the properties of cos−1x. …
