SOLUTION: I don't really know the topic. Arrange the expressions in increasing order of their values. 1.cos(52.5)cos(7.5) 2.sin(52.5)cos(7.5) 3.sin(52.5)sin(7.5) 4.cos(52.5)sin(7.5

Question 1169143: I don't really know the topic.
Arrange the expressions in increasing order of their values.
1.cos(52.5)cos(7.5)
2.sin(52.5)cos(7.5)
3.sin(52.5)sin(7.5)
4.cos(52.5)sin(7.5)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

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.

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 , which is about 0.7.

So useful estimations are sin(7.5) = 0.1 and sin(52.5) = 0.8.

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 , or about 0.7.

So useful estimations are cos(7.5) = 1 and cos(52.5) = 0.6.

Therefore, we can estimate....

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

Now it is easy to arrange those numbers in increasing order.

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