Question

Consider the statements given below
I. Domain of $\sin x$ is $R$.
II. Range of $\sin x$ is $[-1,1]$.
III. The value of $\sin x$ repeats after an interval of $2 \pi$.
IV. $\sin x$ decreases in second and third quadrant.
Choose the correct option.

• A. Only I, II, and III are correct
• B. Only II and III are correct
• C. Only III and IV are correct
• D. All are correct

Answer 1

Answer: (D)

We know that domain of $\sin x$ is $R$ and range of $\sin x$ is $[-1,1]$. Also, we have seen that the value of $\sin x$ repeats after an interval of $2 \pi$. Using this knowledge we get the graph of $\sin x$ as given below.

Thus, It is clear to say that $\sin x$ decreases in second and third quadrant.