Worlds of David Darling
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  1. In a right triangle, if one of the angles is θ, then the tangent of θ is the ratio of lengths of the side opposite θ to the side next to θ.

  2. A straight line that touches a given curve exactly once, at a given point.
  3. The gradient of the tangent is equal to the instantaneous gradient of the curve at the point of contact.

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