WOLFRAM|DEMONSTRATIONS PROJECT

Cosine and Sine Identities with Dihedral Transformations

​
rotation
0
π/2
π
-π/2
reflection
y = 0
y = x
x = 0
y = -x
angle t
2.92
dihedral transformation: (x, y) ↦ (y, x)
identities: (cos(π/2 - t), sin(π/2 - t)) = (sin(t), cos(t))
The relation between certain cosine and sine identities and certain rotations and reflections in the plane are exhibited. For example,
(cos(t+π/2),sin(t+π/2))
is the same as
(-sin(t),cos(t))
, which is the
π/2
(90°) clockwise rotation,
(x,y)↦(-y,x)
, of the point
(cos(t),sin(t))
.