SOLUTION: Which of the following is correct? (a) cos(.1) < sin(.1) < sin(.1)cos(.1) (b) sin(.1)cos(.1) < sin(.1) < cos(.1) (c) cos(.1) < sin(.1)cos(.1) < sin(.1) (d) sin(.1) < co

Algebra ->  Trigonometry-basics -> SOLUTION: Which of the following is correct? (a) cos(.1) < sin(.1) < sin(.1)cos(.1) (b) sin(.1)cos(.1) < sin(.1) < cos(.1) (c) cos(.1) < sin(.1)cos(.1) < sin(.1) (d) sin(.1) < co      Log On


   

Question 675195: Which of the following is correct?
(a) cos(.1) < sin(.1) < sin(.1)cos(.1)
(b) sin(.1)cos(.1) < sin(.1) < cos(.1)
(c) cos(.1) < sin(.1)cos(.1) < sin(.1)
(d) sin(.1) < cos(.1) < sin(.1)cos(.1)
(e) sin(.1) < sin(.1)cos(.1) < cos(.1)

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
For x's less than pi%2F4, cos(x) > sin(x). So this rules out (a) and (c) since they have cos < sin. So only (b), (d) or (e) can be correct.

Next, when a number is multiplied by a number between 0 and 1, the result is smaller. (Remember this if/when you take the SAT!) cos(.1) and sin(.1) are both numbers between 0 and 1. So when we multiply cos(.1)*sin(.1) we end up with a result that is smaller than both!

So the product of cos(.1) and sin(.1) is the smallest number, cos(.1) is the largest and sin(.1) will be the in-between number. Answer (b) has these in the right order.