Question

Which among the following is/are true?
I. The values of 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 $x$ repeat after an interval of $\pi$.

• A. I is true
• B. II 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 $y=\cot x, y= cosec x$ 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 $cosec \,x$ repeat after an interval of $2 \pi$ by using above graph of $y = cosec \,x .$ 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.