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 presented graph displays inverse trigonometric and trigonometric functions. The function $y = \sin^{-1} x$ (inverse sine) is defined on the domain $[-1, 1]$ and has a range of $[-\frac{\pi}{2}, \frac{\pi}{2}]$. Its graph is an increasing curve. The function $y = \sin x$ (standard sine) oscillates between $-1$ and $1$ with a period of $2\pi$. The graph aligns with the characteristics of both $y = \sin^{-1} x$ and $y = \sin x$. Consequently, option (3) is the correct identification.