Graphing sec, csc, cot functions Quiz 1

Question 1

Number of solutions of the equation $$\cot \left( \dfrac{	heta }{2} ight)=\left( 1+\cot \left( 	heta  ight) ight)	ext{ in }\left( -2\pi ,\pi  ight)	ext{ is}$$

Accepted Answer

$$2$$

Answer

$$0$$

Answer

$$1$$

Answer

$$3$$

Question 2

Number of solutions of equation $${{e}^{x}}=\cot \left( x \right)$$ in the interval $$\left[ 0,\dfrac{\pi }{2} \right]$$  is

Accepted Answer

$$1$$

Answer

$$3$$

Answer

$$2$$

Answer

$$4$$

Question 3

Find the value of $$a+b$$ if the following graph as the form $$\sec ax+b$$. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/fb44f9aa-2ff2-4f44-b203-8a0da8550e666965630415217039531.png"/>

Accepted Answer

$$\dfrac{7}{2}$$

Answer

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

Answer

$$\dfrac{5}{2}$$

Answer

$$5$$

Question 4

The number of solutions of the equation given by $$\sin 	heta ={{\sec }^{2}}4	heta $$ in $$\left[ 0,\pi  ight]$$ is/are:

Accepted Answer

$$1$$

Answer

$$3$$

Answer

$$2$$

Answer

$$0$$

Question 5

Number of solutions of the $$	ext{max}\left\{ \operatorname{cosec}x,\sec x ight\}=\sqrt{2}$$ in $$\left[ 0,\pi  ight]$$  is/are

Accepted Answer

$$2$$

Answer

$$4$$

Answer

$$3$$

Answer

$$1$$