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Math Help - I need help understanding this example in my book.

  1. #1
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    Smile I need help understanding this example in my book.

    I don't what they are trying to say. PLEASe help me

    If A falls on Quadrant II and B falls in Quadrant III, then what the sign of cos(A+B).

    its is greater than 0 or less than 0.



    and then another example just like the same.

    If A falls on Quadrant II, and B falls on Quadrant III, then what is the sign of sin(A-B)
    it's is greater than 0 or less than 0.
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  2. #2
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    Re: I need help understanding this example in my book.

    Hello, TrimHonduras!

    \text{If }A\text{ is in Quadrant II and }B\text{ is in Quadrant III,}
    . . \text{what is the sign of }\cos(A+B)\,?

    \begin{array}{cccccccccc}A \in \text{Q II} & 90^o &<& A &<& 180^o \\ B \in \text{Q\,\!III} & 180^o &<& B &<& 270^o \\ \text{Add:} & 270^o &<& A+B &<& 450^o \end{array}

    Hence, A+B is in Quadrant I or IV.

    Therefore:- \cos(A+B) is positive.




    \text{If }A\text{ is in Quadrant II and }B\text{ is in Quadrant III,}
    . . \text{what is the sign of }\sin(A-B)\,?

    We have:- \begin{Bmatrix}90^o &<& A &<& 180^o \\ 180^o &<& B &<& 270^o \end{Bmatrix}

    The minimum difference is when A = 180^o and B = 180^o.
    . . Hence: . A-B \:=\:0^o

    The maximum difference is when A = 90^o and B = 270^o.
    . . Hence:- A-B \:=\:-180^o

    Then:- -180^o \:<\:A-B \:<\:0^o

    Hence, A-B is in Quadrant III or IV.

    Therefore:- \sin(A-B) is negative.
    Thanks from TrimHonduras
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  3. #3
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    Re: I need help understanding this example in my book.

    thank you so much... Now I understand
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