Question

Which of the following is least ? (All angles have been measured in radians)

• A. sin3
• B. sin2
• C. sin1
• D. sin7

Answer 1

The correct option is A sin3

$\sin 3=\sin [\pi -(\pi -3)]=\sin (\pi -3)\approx \sin \left(0.14\right)$

$\sin 2=\sin [\pi -(\pi -2)]=\sin (\pi -2)\approx \sin \left(1.14\right)$

$\sin 7=\sin [2\pi +(7-2\pi )]=\sin (7-2\pi )\approx \sin \left(0.72\right)$

now $1.14>1>0.72>0.14$

$\Rightarrow \sin \left(1.14\right)>\sin 1>\sin \left(0.72\right)>\sin \left(0.14\right)$[ as $1.14,1,0.72,1.14$ lie in the first quadrant and sine functions increase in the first quadrant ]

$\sin \left(1.14\right)>\sin 1>\sin \left(0.72\right)>\sin \left(0.14\right)$
Hence, $sin3$ is least.