MCQ
Which of the following is correct
  • A
    $sin1 > sin2 > sin3$
  • B
    $sin1 < sin2 < sin3$
  • C
    $sin1 < sin3 < sin2$
  • $sin3 < sin1 < sin2$

Answer

Correct option: D.
$sin3 < sin1 < sin2$
d
We know: 1 radian $=\pi / 180=57.295$ degrees

$\sin 1( rad )=\sin 57.295( deg )$

$\sin 2(r a d)=\sin 114.591(\operatorname{deg})$

$\sin 3(r a d)=\sin 171.887(\operatorname{deg})$

These three angles are in 1 st and IInd quadrants

And $\sin \theta=\sin (180-\theta)$

On the curve $y=\sin x$ as we move towards $\pi / 2$ we get the same value.

$\sin (114.591)=\sin (65.409)$ and $\sin (171.887)=\sin (8.113)$

Hence $\sin 3<\sin 1<\sin 2$

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