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Math Help - Find the exact value of the following:

  1. #1
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    Find the exact value of the following:

    cos^2 (pi/8) - 1/2 (a bit tricky)
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  2. #2
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    Re: Find the exact value of the following:

    Quote Originally Posted by boltage619 View Post
    cos^2 (pi/8) - 1/2 (a bit tricky)
    cos \left ( \frac{\pi}{4} \right ) = \frac{\sqrt{2}}{2}

    Now, pi/8 is 1/2 of pi/4. What does the half angle formula for cosine give you?

    -Dan
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  3. #3
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    Re: Find the exact value of the following:

    Well this is how my professor did it and i'm just confused on how she did it, she didn't use the half angle formula.

    Find the exact value of the following:-20.png
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    Re: Find the exact value of the following:

    I'm not sure where you're coming from. Do you know the answer already, is this just a little puzzle for us?

    If not, what do you know about trig that might help you? I notice we have a cos^2, which suggests a half-angle identity, and a pi/8 (half of a half of a half), which again suggest a half-angle identity. Do you know those identities? If you don't, you can find them online if necessary and work this out.
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  5. #5
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    Re: Find the exact value of the following:

    Use the half angle identities: cos 2A = 2(cosA)^2 - 1
    cos pi/4 = 2 ( cos pi/8)^2 - 1 OR ( cos pi/8)^2 = [ cos pi/4 + 1 ]/ 2 Now just plugin the value of cos pi/4 and simplify
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  6. #6
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    Re: Find the exact value of the following:

    Cos 2A = 2cos^2 A -1 comes from the double-angle identity. And thanks for trying to help me out!
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