 mathdynamics

# Derivative of implicite function.

Let consider the equation We know that the set of solution of this equation is the set of points in plane at distance 1 from the origin, or a circle of radius 1 with center in (0,0).
We want to give a description of this set depending on a single variable instead of two.
This is possible only local ,not for the whole set of solutions.
But the collection of local solutions can give us a complete information about the circle.
Let with and For in a small neighborhood of we have # In a triangle the sum of the angles is 180

In any triangle the sum the angles is 180.

In triangle ABC: Proof
Let consider line DE by A parallel to BC
Then and but .

# Definition of Angle

An angle is formed by two rays that have a common origin.

Two intersecting lines form 4 angles. The opposing ones are congruent and the neighboring ones have the sum 180 (are supplementary angles).

AEC = DEB
AED = CEB

AEC + AED = 180
CEB + BED = 180
AEC + CEB = 180
DEA + BED = 180 