# Tangents to curves in the plane: tangent

### 13.7.7 Tangents to curves in the plane: tangent

See Section 14.6.3 for tangents in space.

The tangent command finds tangents to curves.

- tangent takes one or two arguments:
  - C, a curve.
  - p, a point.
  or
  - e, a point defined with element (see Section 13.6.15) using a curve and parameter value.

- tangent(C,p) (or tangent(e)) returns and draws the list of lines tangent to the curve passing through the given point.

#### Examples.

- Input:
  tangent(circle(0,1),1+i)
  Output:
- Input:
  t:= element(0..pi,pi/4):; A:= element(circle(0,1),t):; tangent(A)
  Output:

When tangent is called with an element, the tangent will change along with the point on the element.