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Geometry Level 2

Which of the following is true?

(A) $\cos221^o>\sin319^o$

(B) $\cos139^o>\sin221^o$

(D) $\sin221^o>\cos139^o$

(E) $\sin41^o>\cos319^o$

E A D B C

1 solution

Khang Nguyen Thanh
Aug 2, 2015

First, we have $f(x)=\sin x$ increases on $(0^o, 90^o)$ and $g(x)$ decreases on $(0^o, 90^o)$ , so $\sin41^o<\sin45^o=\cos45^o<\cos41^o$ .

We have:

(A) $\cos221^o>\sin319^o \Leftrightarrow -\cos41^o>-\sin41^o \Leftrightarrow \sin41^o>\cos41^o$ , which is not true.

(B) $\cos139^o>\sin221^o\Leftrightarrow -\cos41^o>-\sin41^o \Leftrightarrow \sin41^o>\cos41^o$ , which is not true.

(D) $\sin221^o>\cos139^o\Leftrightarrow -\sin41^o>-\cos41^o \Leftrightarrow \sin41^o<\cos41^o$ , which is true .

(E) $\sin41^o>\cos319^o\Leftrightarrow \sin41^o>\cos41^o$ , which is not true.

So the correct answer is $\boxed{D}$ .

You had missed to mentioned $g(x) =\cos x$ as it is decreasing in the interval $\,(0°,90°)$ . :)

Naren Bhandari - 3 years, 1 month ago