Question

Which among the following is/are true?
I. The values of $\operatorname{cosec} x$ repeat after an interval of $2 \pi$.
II. The values of $\sec x$ repeat after an interval of $2 \pi$.
III. The values of $\cot x$ repeat after an interval of $\pi$.

• A. 1 is true
• B. 11 is true
• C. III is true
• D. All are true

Answer 1

Answer: (D)

Using behaviour of trigonometric functions we can draw the graphs of $y=\cot x, y=\operatorname{cosec} x$ and $y=\sec x$ as shown below.

So, we see that the values of $\cot x$ repeat after an interval of $\pi$.

Also, we can see that the values of $\operatorname{cosec} x$ repeat after an interval of $2 \pi$ by using above graph of $y=\operatorname{cosec} x$. Similarly, we can say that the values of $\sec x$ repeat after an interval of $2 \pi$ by using the graph of $y=\sec x$ as shown below.

Hence, it is concluded that all the given statements are true.