Which of the following is true?

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(A) We know that the function $f(x) = \sin\ x$ is increasing in the interval $[0^{\circ}, 90^{\circ}]$.For angles greater than $90^{\circ}$,we use the

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We know that the function $f(x) = \sin\ x$ is increasing in the interval $[0^{\circ}, 90^{\circ}]$.For angles greater than $90^{\circ}$,we use the identity $\sin\ 	heta = \sin(180^{\circ} - 	heta)$.Thus,$\sin\ 95^{\circ} = \sin(180^{\circ} - 95^{\circ}) = \sin\ 85^{\circ}$.Now we compare $\sin\ 85^{\circ}$,$\sin\ 63^{\circ}$,and $\sin\ 1^{\circ}$.Since $85^{\circ} > 63^{\circ} > 1^{\circ}$ and the sine function is increasing in the first quadrant,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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