Which of the following is least?

sin 3

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sin 2

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sin 1

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sin 7

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Solution

The correct option is A $sin 3$
a. $sin 3 = sin [π - (π - 3)] = sin (π - 3) = sin (0.14)$
b. $sin 2 = sin [π - (π - 2)] = sin (π - 2) = sin (1.14)$
d. $sin 7 = sin [2 π + (7 - 2 π)] = sin (7 - 2 π) = sin (0.72)$
Now $1.14 > 1 > 0.72 > 0.14$
$\Rightarrow$ $sin (1.14) > sin 1 > sin (0.72) > sin (0.14)$
As $1.14, 1, 0.72, 0.14$ lie in the first quadrant and sine functions increase in the first quadrant]
Hence, $sin 3$ is least.

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Similar questions

\frac{sin 1^{\circ} + sin 3^{\circ} + sin 5^{\circ} + sin 7^{\circ}}{cos 1^{\circ} cos 2^{\circ} sin 4^{\circ}}

sin $1^{\circ}$ $\times$ sin $2^{\circ}$ $\times$ sin $3^{\circ}$ $\times$ …….. $\times$ sin $180^{\circ}$ is equal to:

sin 1^{\circ} sin 2^{\circ} sin 3^{\circ} . . . . . . sin 180^{\circ}

(sin 1^{\circ}) (sin 3^{\circ}) (sin 5^{\circ}) (sin 7^{\circ}) . . . . . . . . . (sin 89^{\circ}) = \frac{1}{2^{n}},

x = sin 1, y = sin 2; z = sin 3

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