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Math Help - Need your help about sinus and cosine!

  1. #1
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    Need your help about sinus and cosine!

    I need your help for these problems:
    1.Which is the max and min value of this function:
    a) y=1/(2+sinx) b)y=sin(cosx) c)y=3sin(x+5)
    2.Solve this equation:
    sinx+siny=2
    3.Demonstrate that in the trigonometric circle tgx=y(T)
    Sorry for my english.
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  2. #2
    Moo
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    Hello,

    y=1/(2+sinx)
    Remember that -1<sin(x)<1
    So 1<2+sin(x)<3

    As 2+sin(x) is always positive, 1>1/(2+sin(x))>1/3

    And you have the min & max

    y=sin(cosx)
    -1<cos(x)<1

    But -1>-pi/2 and 1<pi/2, and we know that sin is an increasing function in [-pi/2,pi/2]
    So sin(-pi/2) < sin(-1) < sin(cos(x)) < sin(1) < sin(pi/2)



    For the third one, it's basic if you use the condition of the first question.
    For the fourth one, it's also the same property you'll have to use.
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