Question

Which of the following is possible?

• A.
  $\sin \theta =\frac{5}{3}$
• B.
  $\tan \theta =1002$
• C.
  $\mathrm{cosec}\theta =\frac{1}{2}$
• D.
  $\cos \theta =\frac{3}{5}$

Answer 1

Answer: (B), (D)

The correct options are
B
$\tan \theta =1002$
D

$\cos \theta =\frac{3}{5}$
This question is based on Range of the various trigonometric function.
a. For $\sin \theta =\frac{5}{3}$. It is not possible as $-1\le \sin \theta \le 1$ and here $\sin \theta =\frac{5}{3}>1$.
b. $\tan \theta =1002$ is possible as $\tan \theta$can take any real value.
c. $\mathrm{cosec}\theta =\frac{1}{2}$ is not possible as $\mathrm{cosec}\theta \in (-\infty ,-1]\cup [1,\infty ).$
d. $\cos \theta =\frac{3}{5}$ is possible as $\cos \theta \in \left(-1,1\right]$
Hence, Options b. and d. are correct.