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Math Help - Find equation of the sides of a square

  1. #1
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    Find equation of the sides of a square

    A vertex of a square of side a is at the origin. The inclination of one of its sides is θ. Find the equations of the sides of the square.
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  2. #2
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    Hello, ling_c_0202!

    A vertex of a square of side a is at the origin.
    The inclination of one of its sides is \theta.
    Find the equations of the sides of the square.

    First of all, there are two possible squares . . . I'll pick one of them.
    Code:
                      |        C  a sinθ
                      |         o - - - +
                      |   *      *      :
              D     * |           *     :
              o       |            *    : a cosθ
              :*      |             * θ :
              : *     |              *  :
              :  *    |               * :
              : θ *   |                *:
       a cosθ :    *  |                 o B
              :     * |           *     :
              :      *|     *  θ        : a sinθ
          - - + - - - o - - - - - - - - + - - -
               a sinθ A      a cosθ

    Vertex A:\;(0,\,0)

    Vertex B:\;(a\cos\theta,\,a\sin\theta)

    Vertex C:\;(a\cos\theta-a\sin\theta,\,a\sin\theta+a\cos\theta)

    Vertex D:\;(-a\sin\theta,\,a\cos\theta)


    I'll let you write the equations of the lines . . .

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