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Math Help - Cos theta = -Sin theta

  1. #1
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    Cos theta = -Sin theta

    For what angles theta B/T 0 & 360 does cos theta = -sin theta?

    It's simple question, but I could not think of any angles that would make this statement true. Maybe I'm missing something...
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  2. #2
    MHF Contributor ebaines's Avatar
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    Here's a hint -- there are two places between 0 and 360 degrees where cos(theta) = -sin(theta). Can you see that at 45 degrees cos(theta) = sin(theta)? For this angle you are in quadrant 1, where both sin and cos are positive. But what about other quadrants where sin and cos have opposiite signs? I trust this helps - now post back with what you think the answer is.
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  3. #3
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    Yes. They would have opposite sings in Q1 and Q4, when dealing with 45 reference.
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  4. #4
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    Cos\theta in a unit circle gives the x co-ordinate of a point on the circumference.

    Sin\theta gives the y co-ordinate of the same point.

    -Sin\theta is the negative of the y co-ordinate.

    To be equal numerically, the angles cut the quadrants in two equal parts,
    hence the angles are 45, 135, 225 and 315 degrees.

    For 2 of these, the x and y co-ordinates of the 4 points are equal numerically and have opposite sign.

    In which quadrants are the co-ordinates of opposite sign?
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  5. #5
    Super Member General's Avatar
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    cos(\theta)=-sin(\theta)
    cot(\theta)=-1
    tan(\theta)=-1
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