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Math Help - Find the value

  1. #1
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    Find the value

    Hey everyone, I couldn't figure out how how to find the value for:



    I know the answer, but, I'm looking for the solution, and why.

    Thanks
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  2. #2
    Junior Member Barioth's Avatar
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    Re: Find the value

    Hi you'll need your trigo circle to get this one.

    If you look at the circle you'll notice that

    Sin(\frac{\pi}{2}-x)=cos(x)

    There is also a proof if you use the fact

    sin(a-b)=cos(b)sin(a)-cos(a)sin(b).

    Try it now, let me know if you can't make it!
    Thanks from Imonars
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  3. #3
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    Re: Find the value

    Nope, sorry I have no idea how to do it. but, my professor did it like this:
    1 + sin^2 79 cos^2 7
    1 + 1 = 2

    I think he did something wrong tho..
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  4. #4
    Junior Member Barioth's Avatar
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    Re: Find the value

    mhm maybe you prof is wrong stick with me and we shall know!

    First:
    Quote Originally Posted by Barioth View Post
    Sin(\frac{\pi}{2}-x)=cos(x)
    Do you understand this?
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  5. #5
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    Re: Find the value

    Quote Originally Posted by Imonars View Post
    Nope, sorry I have no idea how to do it. but, my professor did it like this:
    1 + sin^2 79 cos^2 7
    1 + 1 = 2
    I think he did something wrong tho..

    I think you may have copied incorrectly.

    \sin(7^o)=\cos(83^o) so 1+\cos^2(83^o)+\sin^2(83^o)=2
    Thanks from Imonars
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  6. #6
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    Re: Find the value

    I never copy wrong from the board, i always triple check my notes. This is not the first time he make these kinds of mistakes.. anyways Thanks guys I got it from Plato. and barioth, Yes I do understand that part, it's a formula
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  7. #7
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    Re: Find the value

    Hello, Imonars!

    \text{Simplify: }\:1 + \sin^2(7^o) + \sin^2(83^o)

    \text{Note that: }\:\sin(83^o) \;=\;\sin(90-7) \;=\;\sin(90^o)\cos)7^o - \cos(90^o)\sin(7^o)

    . . . . . . . . . . . . . . . =\;1\!\cdot\!\cos(7^o) - 0\!\cdot\!\sin(7^o) \;=\;\cos(7^o)


    \text{The expression becomes: }\:1 + \underbrace{\sin^2(7^o) + \cos^2(7^o)}_{\text{This is 1}} \;=\; 2
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  8. #8
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    Re: Find the value

    That's it! Thank you all and thank you soroban that's exactly what I was looking for!
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