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Math Help - a couple tricky trig function problems

  1. #1
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    a couple tricky trig function problems

    1) express as a sum or difference as it applies to: sin(5x)sin(3x)

    2) find the exact value in radical form for: cos(45)cos(15)

    I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.

    Thanks ahead of time. This site is very, very helpful.
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  2. #2
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    Quote Originally Posted by GUNSLINGAZ View Post
    1) express as a sum or difference as it applies to: sin(5x)sin(3x)

    2) find the exact value in radical form for: cos(45)cos(15)

    I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.

    Thanks ahead of time. This site is very, very helpful.
    For Q1, you should have a formula somewhere which gives an expression for sin A x sin B. Find that first then sub in 5x for A and 3x for B.

    For Q2, use a similar expression for cos A x cos B, sub in appropriate values and then simplify.

    You should know sin, cos, tan of 30, 45 and 60 off by heart.

    If you don't, I suggest you do this:

    Draw an equilateral triangle - let each side be length 2 - slice it down the middle - you now have a 30, 60, 90 triangle with the hypotenuse 2, base 1 - use Pythagoras to work out the other side is sqrt(3) - mark in your angles. You can then read off sin, cos, tan of 30 and 60 degrees.

    For 45 degrees, draw a right-angled isoceles triangle with side lengths and (by Pythagoras) hypotenuse is sqrt(2). Label angles - read off sin, cos tan of 45 degrees.
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  3. #3
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    Quote Originally Posted by GUNSLINGAZ View Post
    1) express as a sum or difference as it applies to: sin(5x)sin(3x)

    2) find the exact value in radical form for: cos(45)cos(15)

    I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.

    Thanks ahead of time. This site is very, very helpful.
    hi

    in general ,

    sin A sin B = -(1/2)[cos (A+B)-cos (A-B)]

    cos A cos B=(1/2)[cos (A+B)+cos (A-B)]
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  4. #4
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    thanks so much. in looking at my handout, i know see the identities you mention under "product to sum identities." thanks.
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  5. #5
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    find the exact value in radical form for: cos(45)cos(15)
    cos(a-b) = cosacosb+sinasinb
    = cos(45)*(cos(45-30))
    = cos(45)*(cos45cos30+sin45sin30)
    rest is numerical
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