CBSE 2025, Set 1

Question

The given graph illustrates:

![Graph of inverse trig function](https://www.edvaya.com/images/cbse/mathematics/2025/set1/q1-inverse-trig-graph.webp)

*(The graph passes through the origin, has horizontal asymptotes at $y = \pi/2$ and $y = -\pi/2$, and is defined for all real x)* A). $y = 	an^{-1} x$ B). $y = \csc^{-1} x$ C). $y = \cot^{-1} x$ D). $y = \sec^{-1} x$

Edvaya · Accepted Answer

The correct answer is $y = 	an^{-1} x$. The graph of $y = 	an^{-1} x$ has the following characteristics that match the given graph: - Domain: all real numbers $(-\infty, \infty)$ - Range: $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}ight)$ — horizontal asymptotes at $y = \dfrac{\pi}{2}$ and $y = -\dfrac{\pi}{2}$ - Passes through the origin $(0, 0)$ - Strictly increasing, S-shaped curve The other options have different domains/ranges: - $\csc^{-1} x$: defined only for $|x| \geq 1$ - $\cot^{-1} x$: range is $(0, \pi)$, not $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}ight)$ - $\sec^{-1} x$: defined only for $|x| \geq 1$

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Mathematics > Trigonometry > Inverse Trigonometric Functions

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