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Trigonometry, different products of sine and cosine

  1. Sep 22, 2007 #1
    1. The problem statement, all variables and given/known data

    There is a right angled triangle, with the following angles, a, b, and 90deg.

    If a < b, how many different values are there among the following expressions?

    sin a sin b, sin a cos b, cos a sin b, cos a cos b

    2. Relevant equations



    3. The attempt at a solution

    I dont really know any trigonometric identies and im guessing thats where the solution lies :S
     
    Last edited: Sep 23, 2007
  2. jcsd
  3. Sep 22, 2007 #2
    Here is a trigonometric identity: sin(x) = cos(90 - x)
    Try to use it.
     
  4. Sep 23, 2007 #3
    :S

    sorry i still dont know how i would use it
     
  5. Sep 23, 2007 #4
    What is the sum of the 3 angles in a triangle?
    And if you know that one of them is a right angle, then what is the sum of the other 2?
     
  6. Sep 23, 2007 #5

    HallsofIvy

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    The point is that sin(a)= cos(b) and sin(b)= cos(a).
     
  7. Oct 9, 2007 #6
    there are 3 different values there. the oiint in telling you that b>a is to make sure you know that b does not equal to a. because, is b=a, the values for all the expressions will be the same. but in this case, since the 2 angles are different, sina=cosb. also, sinb=cosa. if you don't get this, try drawing out a right-angled triangle and label it's angles. use 3,4,5 as the length of its sides. 5 is the hypothenus. then sub the values into the expressions. you will find that sina sinb=cosa cosb.
     
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