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Question
Which of the following is correct?
Options
- \[\sin1^\circ > \sin1\]
- \[\sin1^\circ < \sin1\]
- \[\sin1^\circ = \sin1\]
- \[\sin1^\circ = \frac{\pi}{180}\sin1\]
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Solution
We know that, 1 radian is approximately 57º.
Also, the value of sin x is always increasing for \[0 \leq x \leq 90^\circ\] ( or sin x is an increasing function for \[0 \leq x \leq 90^\circ\] ).
Now,
\[1^\circ < 57^\circ\]
\[Or 1^\circ < 1\text{ radian }\]
\[ \therefore \sin1^\circ < \sin1\]
Hence, the correct answer is option \[\sin1^\circ < \sin1\].
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