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Math Help - Sum Difference Identities

  1. #1
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    Sum Difference Identities

    There is a section on my worksheet that says
    "Rewrite each expression in terms of the sine, cosine, or tangent using the addition and subtraction identities. Simplify each result."

    I don't understand what I am suppose to do for that section.
    first two problems:
    sin(5pi/2 + t)

    cos (pi/6-t)

    and one more thing for another section i am suppose to be finding sin2t cos2t and tan2t

    if sin t = 4/5, t in Q I
    is this correct
    sin2t = 8/5

    cost2t = 6/5

    tan2t = 8/3???

    thanks in advance
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  2. #2
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    do you know the sum/difference identities for sine, cosine, and tangent ? they should be listed in your text.

    \sin\left(\frac{5\pi}{2} + t\right) = \sin\left(\frac{5\pi}{2}\right)\cos(t) + \cos\left(\frac{5\pi}{2}\right)\sin(t) = (1) \cdot \cos(t) + (0) \sin(t) = \cos(t)

    look up the difference identity for cosine and determine \cos\left(\frac{\pi}{6} - t\right)

    if \sin(t) = \frac{4}{5} , then \sin(2t) \neq \frac{8}{5}

    \sin(2t) = sin(t+t) ... use the sum identity for sine to determine the double angle identity for sine.
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  3. #3
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    ok for cos(pi/6-t)

    im at radical3/2 x cos(t) + 1/2 x sin(t)

    what do i do after that?
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  4. #4
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    also sin(t+t) for 4/5 is 24/25?
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  5. #5
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    Quote Originally Posted by cokeclassic View Post
    ok for cos(pi/6-t)

    im at radical3/2 x cos(t) + 1/2 x sin(t)

    what do i do after that?
    nothing ... you're done.



    Quote Originally Posted by cokeclassic View Post
    also sin(t+t) for 4/5 is 24/25?
    yes
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