Hello, ling_c_0202!
A vertex of a square of side $\displaystyle a$ is at the origin.
The inclination of one of its sides is $\displaystyle \theta$.
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 $\displaystyle A:\;(0,\,0)$
Vertex $\displaystyle B:\;(a\cos\theta,\,a\sin\theta)$
Vertex $\displaystyle C:\;(a\cos\theta-a\sin\theta,\,a\sin\theta+a\cos\theta)$
Vertex $\displaystyle D:\;(-a\sin\theta,\,a\cos\theta)$
I'll let you write the equations of the lines . . .