True.. because you can imagine a disk with a rod connected to it..the disk rotation in the Z axis. Now imagine that the rod is always oriented vertically, always parallel to the vertical as the disk rotates..this means that the motion at the tip of the rod will look like a circle too. sinusoidal.
So that's like a connecting rod with infinite length. since it forms a "triangle" of infinite height, it's almost as if the sides were parallel like the example above. Hence he motion would be sinusoidal.
This is another way to see it without equations: