Which of the following is true?

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(A) To compare the values,we convert the angles to the first quadrant.$\sin\ 95^{\circ} = \sin(180^{\circ} - 95^{\circ}) = \sin\ 85^{\circ}$.Now we co

Vedclass · Accepted Answer

$\sin\ 95^{\circ} > \sin\ 63^{\circ} > \sin\ 1^{\circ}$

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(A) To compare the values,we convert the angles to the first quadrant.$\sin\ 95^{\circ} = \sin(180^{\circ} - 95^{\circ}) = \sin\ 85^{\circ}$.Now we compare $\sin\ 85^{\circ}$,$\sin\ 63^{\circ}$,and $\sin\ 1^{\circ}$.Since the sine function is strictly increasing in the interval $[0^{\circ}, 90^{\circ}]$,we have $\sin\ 85^{\circ} > \sin\ 63^{\circ} > \sin\ 1^{\circ}$.Therefore,$\sin\ 95^{\circ} > \sin\ 63^{\circ} > \sin\ 1^{\circ}$.

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