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Math Help - Trig Function Proofs

  1. #1
    Member realintegerz's Avatar
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    Trig Function Proofs

    Need some help on proving these, I know pythagorean identities, but I'm lost on these, I know that cos(x) = cos(-x)

    1) If cos( alpha + beta) = cos (alpha) cos (beta) - sin(alpha) sin (beta), show that cos (2t) = cos^2 (t) - sin^2 (t)

    2) If sin (alpha + beta) = sin (alpha) cos(beta) + cos (alpha) sin (beta), show that sin (2t) = 2 sin (t) cos (t)

    and also if anyone can help on these that would be great too

    3. Find all values that sin (alpha) = sin (2 alpha)

    4. Find all values that cos (2 alpha) = cos (alpha)

    5. Show cos^2 (t) = [1 + cos (2t)]/2

    6. Show sin^2 (t) = [1 - cos (2t)]/2
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  2. #2
    Member
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    Quote Originally Posted by realintegerz View Post
    Need some help on proving these, I know pythagorean identities, but I'm lost on these, I know that cos(x) = cos(-x)

    1) If cos( alpha + beta) = cos (alpha) cos (beta) - sin(alpha) sin (beta), show that cos (2t) = cos^2 (t) - sin^2 (t)
    Let alpha = t, and let beta = t. Plug them into the formula that you have.

    2) If sin (alpha + beta) = sin (alpha) cos(beta) + cos (alpha) sin (beta), show that sin (2t) = 2 sin (t) cos (t)
    Again, let alpha = t, and let beta = t. Plug them into the formula that you have.

    3. Find all values that sin (alpha) = sin (2 alpha)
    replace the right side using the identity that you have from problem 2). then, divide both sides by sin(alpha) [there is something extra you have to do because you do this, check your notes] and then solve for x.

    There are a few starts. It sounds like you are a ways behind in this class. You need to close the gap quickly. I personally feel that trig proofs and trig solving are some of the tougher concepts you're going to see this year because they are very unforgiving of being set aside to be done later.
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