trig

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find the exact value of cos 3.14/8

  • trig -

    Since 3.14 is an approximation to π,
    I suppose you mean finding the exact value of cos(π/8).

    Use the half angle formulae:
    cos²(x/2)=(1+cos(x))/2...(1)
    sin²(x/2)=(1-cos(x))/2...(2)
    The second formula is not required for this problem, but I suggest you memorize both of them, because they will be very useful in your academic life.
    Start from known values,
    cos(π/2)=0
    cos²(π/4)=(1+0)/2
    cos(π/4)=(√2)/2
    Apply the formula one more time to get cos(π/8):
    cos²(π/8)=(1+(√2)/2))/2
    cos(π/8)=√(2+√2)/2

  • trig -

    Okay, I understand how to get pi/8 but how do you figure pi/7 and how do you figure cos(10degrees) when you can use the sum and difference method of angles? Please help it is driving me crazy, and I have finals coming up. Need to get this down. Can I do the method about using pi/3 and pi/4 in the half angle formulas to find exact value of cos and sin of (pi/7)? I am so confused.

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