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Math Help - re:simplifying trig

  1. #1
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    re:simplifying trig

    Hello.
    I am trying to simplify the following -
    cos40cos20-sin40sin20
    I can see that I have cos60 and sin60, which is 1/2 and √3/2, respectively.
    However, the answer only requires that I give 1/2, and not √3/2?
    Thanx
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  2. #2
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    Quote Originally Posted by morelemonzanybody? View Post
    Hello.
    I am trying to simplify the following -
    cos40cos20-sin40sin20
    I can see that I have cos60 and sin60, which is 1/2 and √3/2, respectively.
    However, the answer only requires that I give 1/2, and not √3/2?
    Thanx
     \cos A \cos B - \sin A \sin B = \cos (A+B)
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  3. #3
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    re: addition formulae

    Hi:
    thanks for your answer:
    I am aware of the addition formulae.
    For this problem, I can get the answer from simply inputting everything into the calculator. However, I fail to understand how to do this problem by hand.
    I know that this represents a right-angled triangle. And that I take the values from the lengths of the triangle (or in this case the angle), but why is the answer just 'cos=xxxxx'?
    Is it like this?
    cos(40)=0.7660444431 x cos(20)=0.9396926208 - sin(40)=0.6427876097 x sin(20)=0.3420201433 = 1/2
    This seems awfully long winded to do by hand.
    And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?
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  4. #4
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     <br />
sin(90-\theta) = cos(\theta) <br />

    I can see that I have cos60 and sin60, which is 1/2 and √3/2, respectively.

    sin(60) =√3/2= cos(30)

    cos(60) = 1/2 = sin(30)

    And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?

    Use the above thing to write it in cos()= "xxxxx"

    Incase this is not what you are asking please make question a bit clear
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  5. #5
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    reply

    well:
    I guess what I'm trying to say is that I really don't understand the steps they have taken in the problem. I must be missing the point.
    So, do I:
    1/ add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.
    2/ take cos60 to be 1/2, and sin60 to be √3/2
    3/ but that means 1/2 - √3/2, which is wrong.

    or,
    1/ add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.
    2/ cos60sin30-sin60cos30, which is 1/2 x 1/2 - √3/2 x √3/2 = -1/2
    The right answer but negative instead of positive.
    And, why is the answer sin=1/2, and not cos=1/2
    I'm really getting confused here
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  6. #6
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    Quote Originally Posted by morelemonzanybody? View Post
    Hi:
    thanks for your answer:
    I am aware of the addition formulae.
    For this problem, I can get the answer from simply inputting everything into the calculator. However, I fail to understand how to do this problem by hand.
    I know that this represents a right-angled triangle. And that I take the values from the lengths of the triangle (or in this case the angle), but why is the answer just 'cos=xxxxx'?
    Is it like this?
    cos(40)=0.7660444431 x cos(20)=0.9396926208 - sin(40)=0.6427876097 x sin(20)=0.3420201433 = 1/2
    This seems awfully long winded to do by hand.
    And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?
    There are only two steps necessary:

     \cos(40)\cos(20) - \sin(40)\sin(20) = \cos(40+20) = \cos(60)

    Now, look at the attached triangle to find  \cos(60)

    You should find  \cos(60) = \frac{1}{2} , and that's it! Game over.
    Attached Thumbnails Attached Thumbnails re:simplifying trig-tyguhijop.jpg  
    Last edited by Mush; February 24th 2009 at 04:16 AM.
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  7. #7
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    Quote Originally Posted by morelemonzanybody? View Post
    Hi:
    thanks for your answer:
    I am aware of the addition formulae.
    For this problem, I can get the answer from simply inputting everything into the calculator. However, I fail to understand how to do this problem by hand.
    I know that this represents a right-angled triangle. And that I take the values from the lengths of the triangle (or in this case the angle), but why is the answer just 'cos=xxxxx'?
    Is it like this?
    cos(40)=0.7660444431 x cos(20)=0.9396926208 - sin(40)=0.6427876097 x sin(20)=0.3420201433 = 1/2
    This seems awfully long winded to do by hand.
    And, what happens in a question like sincos+sincos. Is this answer sin=xxxx, just because the question starts with sin?
    With \sin(A)\cos(B) + \sin(B)\cos(A), you can simplify to  \sin(A+B)
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  8. #8
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    1 add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.
    Cos(a) +cos(b) is not equal to cos(a+b)
    sin(a)+sin(b) is not equal to sin(a+b)

    2 take cos60 to be 1/2, and sin60 to be √3/2
    its a fact that cos(60degrees) = 1/2 and sin(60degrees) = √3/2
    Don't take it as assumption

    3 but that means 1/2 - √3/2, which is wrong.
    Yes its wrong!!!!


    1 add the cos20cos40 to get cos60, and the sin40sin20 to get sin60.

    Cos(a) +cos(b) is not equal to cos(a+b)
    sin(a)+sin(b) is not equal to sin(a+b)

    2 cos60sin30-sin60cos30, which is 1/2 x 1/2 - √3/2 x √3/2 = -1/2

    This has no meaning forget this concept


    Now follow Mush
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  9. #9
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    re: the game

    And a fine Game it was too, Mush.
    Arigatogozaimasu
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  10. #10
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    re: the game

    sorry
    should have said:
    arigatogozaimashita
    past tense
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