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Math Help - rotation

  1. #1
    Member Veronica1999's Avatar
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    rotation

    A 15-degree counterclockwise rotation about (4,6) transforms (2,1) onto another point (x,y). Find x and y correct to the three decimal places.

    Pls find attached work. I know I am doing something wrong but i can't figure it out.
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  2. #2
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    Let O (4, 6) be the center. Let A be ( 2,1) and B be ( x, y). Draw a vertical line from O. Draw perpendiculars AD and BE from A and B on the vertical line. Let the angle AOD be θ. Then then angle BOE is equal to ( 15 + θ) degrees. Take tanθ and tan(15 + θ) and proceed.
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  3. #3
    Member Veronica1999's Avatar
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    Thank you for your help.
    i was not sure how to apply tan so I used cos and sin.
    Is my answer correct? And could you show me how to use tan?

    pls find attached work.

    thanks in advance for your time.
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  4. #4
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    Your answer is correct. From the figure you can see that AD = (4-2) and OD = (6- 1).
    so tanθ = 2/5 = 0.4.
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