Question 1169143
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I'm guessing we are supposed to answer this question using estimation and our basic understanding of the sine and cosine functions -- rather than evaluating each expression using a calculator.<br>
The sine function is 0 at 0 degrees and increases to 1 at 90 degrees.  The increase is rapid in the beginning and slow at the end.  At 45 degrees, the sine value is {{{sqrt(2)/2}}}, which is about 0.7.<br>
So useful estimations are sin(7.5) = 0.1 and sin(52.5) = 0.8.<br>
The cosine function is 1 at 0 degrees and decreases to 0 at 90 degrees.  The decrease is very slow at first and faster at the end.  At 45 degrees, the cosine value is also {{{sqrt(2)/2}}}, or about 0.7.<br>
So useful estimations are cos(7.5) = 1 and cos(52.5) = 0.6.<br>
Therefore, we can estimate....<br>
1. cos(52.5)(cos(7.5) = (0.6)(1) = 0.6
2. sin(52.5)(cos(7.5) = (0.8)(1) = 0.8
3. sin(52.5)(sin(7.5) = (0.8)(0.1) = 0.08
4. cos(52.5)(sin(7.5) = (0.6)(0.1) = 0.06<br>
Now it is easy to arrange those numbers in increasing order.<br>