Question

The following graph is a combination of:

• A. $y = \sin^{-1} x$ and $y = \cos^{-1} x$
• B. $y = \cos^{-1} x$ and $y = \cos x$
• C. $y = \sin^{-1} x$ and $y = \sin x$
• D. $y = \cos^{-1} x$ and $y = \sin x$

Hint:

Inverse trigonometric functions have restricted domains and ranges. The graphs of these functions often appear different from their trigonometric counterparts.

Answer 1

The Correct Option is C

The given graph shows a combination of inverse trigonometric and trigonometric functions.
The function $y = \sin^{-1} x$ is the inverse sine function, which has a restricted domain and range between $[-\frac{\pi}{2}, \frac{\pi}{2}]$ and $[-1, 1]$, respectively. The graph of $y = \sin^{-1} x$ appears as an increasing curve.
The function $y = \sin x$ is the standard sine function, which oscillates between $-1$ and $1$, and has a period of $2\pi$.
The graph shown matches the properties of $y = \sin^{-1} x$ and $y = \sin x$. Therefore, the correct answer is (3).