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Math Help - Finding the rotation in Radians

  1. #1
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    Finding the rotation in Radians

    I am asked to move a triangle so that C is at the origin and CB lies along the positive x-axis.

    The original vertices were A(7,5), B(5,1) and C(-4,2).

    The translated vertices are A(11,3), B(9,-1) and C(0,0). Which is t:4,-2 (x+4, y-2).

    Now, I'm onto the rotation part. How do I find the exact values of cosθ, sinθ and tanθ and hence write down a formal definition of rθ?

    The perplexing part is that the question states that I don't need to work out the angle θ.
    Perhaps a fresh pair of eyes on the question will help (please PM me if you'd like to read the Q in full).

    If you can help me solve this, I will be most grateful.
    Thanks in advance.
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  2. #2
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    Quote Originally Posted by mezhopking View Post
    I am asked to move a triangle so that C is at the origin and CB lies along the positive x-axis.

    The original vertices were A(7,5), B(5,1) and C(-4,2).

    The translated vertices are A(11,3), B(9,-1) and C(0,0). Which is t:4,-2 (x+4, y-2).

    Now, I'm onto the rotation part. How do I find the exact values of cosθ, sinθ and tanθ and hence write down a formal definition of rθ?

    The perplexing part is that the question states that I don't need to work out the angle θ.
    Perhaps a fresh pair of eyes on the question will help (please PM me if you'd like to read the Q in full).

    If you can help me solve this, I will be most grateful.
    Thanks in advance.
    1. Draw a sketch of the situation after the translation.

    2. The slope of the line C'B' correspond to the tangens of the angle of rotation. Since the line passes through the origin you only have to use the coordinates of B'(9, -1):

    \tan(\theta)=\dfrac{-1}9

    All other values follow consequently.

    I've attached a drawing. This drawing was posted a few weeks ago at MHF. Thus your question must be answered somewhere. Search for it.
    Attached Thumbnails Attached Thumbnails Finding the rotation in Radians-transl_drehung_3eck.png  
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  3. #3
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    Thanks for taking the time to reply, it was of great help.
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