Domain and range of sec, csc, cot functions Quiz 1

Question 1

Find the value of $$\csc \left\{ {{\cot }^{-1}}\left( \cot \left( \dfrac{3\pi }{4} \right) \right) \right\}$$, considering the domain and range of the trigonometric functions.

Accepted Answer

$$\sqrt{2}$$

Answer

$$-\sqrt{2}$$

Answer

$$\dfrac{1}{\sqrt{2}}$$

Answer

$$-\dfrac{1}{\sqrt{2}}$$

Question 2

Find the domain of the given figure below.  <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/108a6280-f7a5-42ea-92b2-92055dc752058675921369665752737.png"/>

Accepted Answer

$$\mathbb{R}-\left\{ n\pi  \right\};n=0,1,2...$$

Answer

$$\mathbb{R}$$

Answer

$$\mathbb{R}-\left\{ \left( 2n+1 \right)\dfrac{\pi }{2} \right\};n=0,1,2...$$

Answer

None.

Question 3

Find the domain of $$y=\csc ({{x}^{2}}+5x+2)$$

Accepted Answer

$$\mathbb{R}-\left\{ \dfrac{-5\pm \sqrt{17+4n\pi }}{2} \right\}$$

Answer

$$\mathbb{R}-\left\{ \dfrac{-5+\sqrt{17+4n\pi }}{2} \right\}$$

Answer

$$\mathbb{R}-\left\{ \dfrac{-5-\sqrt{17+4n\pi }}{2} \right\}$$

Answer

None

Question 4

Find the value of $${{\csc }^{-1}}\left( \csc \left( \dfrac{2\pi }{3} \right) \right)$$

Accepted Answer

$$\dfrac{\pi }{3}$$

Answer

$$\dfrac{2\pi }{3}$$

Answer

$$-\dfrac{\pi }{3}$$

Answer

$$-\dfrac{2\pi }{3}$$

Question 5

What will be the value of $$\sec \left( {{\cot }^{-1}}\left( -\dfrac{2}{3} \right) \right)$$ , considering the domain and range of the trigonometric functions.

Accepted Answer

Both (a) and (b)

Answer

$$\dfrac{\sqrt{13}}{2}$$

Answer

$$-\dfrac{\sqrt{13}}{2}$$

Answer

None