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Math Help - trigonometry equation

  1. #1
    seb
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    trigonometry equation

    please help:

    if 0 is smaller then or equal to a which is < then 2pi then the equation sina=cos a has how many solutions? what are they? justify.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by seb View Post
    please help:

    if 0 is smaller then or equal to a which is < then 2pi then the equation sina=cos a has how many solutions? what are they? justify.
    Sketch the curves y=sin(x) and y=cos(x) over the interval (0, 2 pi).

    You will observe that there are two points at which the cross, and the
    x's for these points are the values for which sin(x)=cos(x) and so are
    the values of a that you require.

    sin(a)=cos(a)

    can be rearranged to tan(a)=1, so one solution is 45 degrees (pi/4 radian)

    The other solution is in the third quadrant (where tan is positive) and so
    is 180+45 degrees (pi+pi/4 radian)

    RonL
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  3. #3
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    Hello, seb!

    if 0 < θ < 2π, then the equation sinθ = cosθ has how many solutions?
    What are they? .Justify.

    Divide both sides by cosθ, and we have: .tanθ .= .1

    The only angles on the inteval [0, 2π) with a tangent of 1 are: .π/4 and 5π/4

    Therefore, there are two solutions: .θ .= .π/4, 5π/4

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