Graph of Trigonometric Ratios

Q.

Match the following (Figures are rough sketches)

(i)sinx

(ii) cosx

(iii) tanx

1. i -Q, ii -x, iii -P

2. i -P, ii -Q, iii -R

3. i -R, ii -P, iii -Q

4. i -Q, ii -P, iii -R

Q.

How many of following statements are true?

(1)Period of sin $\theta$ is $\pi$, because sin 0 and sin $\pi$ = 0

(2) Period of cos $\theta$ is $\pi$

(3) Period of tan $\theta$ is $\pi$

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Q.

$\begin{array}{ccc}\text{Function}& \text{Domain}& \text{Range}\\ \text{(i) sinx}& \text{(P) R}& \text{(L) [-1, 1]}\\ \text{(ii) cos x}& \text{(Q) R-n}\pi & \text{(M) R}\\ \text{(iii) tan x}& \text{(R) R- {(2n+1)}}& \text{(N)}(-\infty ,\text{-1]}\cup \text{[1,}\infty )\\ \text{(iv) cosec x}& & \\ \text{(v) sec x}& & \\ \text{(vi) cot x}& & \end{array}$

How many of the following are matched correct?

(i) -P-L, (ii) -P-L, (iii)-R-M, (iv) -Q-N, (v) -R-N, (vi) -Q-M

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Q. $\mathrm{The}\mathrm{function}f\left(x\right)=\mathrm{cosec}x\mathrm{is}\mathrm{discontinuous}\mathrm{at}x=\mathrm{n\pi },n\in Z$.

1. False
2. True

Q. Which of the following is the least?

1. 
   $\sin 3$
2. 
   $\sin 2$
3. 
   $\sin 1$
4. 
   $\sin 7$

Q. Which of the following is possible?

1. 
   $\sin \theta =\frac{5}{3}$
2. 
   $\tan \theta =1002$
3. 
   $\mathrm{cosec}\theta =\frac{1}{2}$
4. 
   $\cos \theta =\frac{3}{5}$

Q. $\mathrm{The}\mathrm{function}f\left(x\right)=\sec x\mathrm{is}\mathrm{continuous}\mathrm{for}\mathrm{all}x\in R.$

1. False
2. True

Q. If $A=2\sin \theta +{\cos }^2\theta$, then which of the following is/are true?

1. 
   Maximum value of $A=5$.
2. 
   Minimum value of $A=-2.$
3. 
   Maximum value of $A$ occurs when $\sin \theta =1.$
4. 
   Minimum value of $A$ occurs when $\sin \theta =-1.$

Q. $\mathrm{The}\mathrm{function}f\left(x\right)=\tan x\mathrm{is}\mathrm{defined}\mathrm{for}x\in R~(2n+1)\frac{\pi }{2},n\in Z$

1. True
2. False

Q. $\mathrm{The}\mathrm{function}f\left(x\right)=\cot x\mathrm{is}\mathrm{defined}\mathrm{for}\mathrm{all}x\in R~\mathrm{n\pi },n\in Z.$

1. False
2. True