# Thread: Find equation of the sides of a square

1. ## 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.

2. 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 . . .