A point on a unit circle carries two coordinates: cosine tells you how far across; sine tells you how far up.
The radius is one, so the horizontal and vertical projections are exactly cosine and sine. Moving around the circle repeats the coordinates every full turn. Tangent is undefined when the horizontal coordinate is zero.
Sine and cosine are coordinates, not lengths that must always be positive.
Drag on the circle or use the angle slider. Tangent is undefined at 90° and 270°.