How is tangent defined

This condition will apply to every point on the line PL except point A. Let the points of contact be A and B, as shown:. Comparing the two triangles , we see that:. Using theorem I, if the radius is drawn to the tangents TP and TQ it will be perpendicular to these tangents.

Example 2: Consider a chord AB of length 10 cm in a circle of radius 6 cm. Tangents at A and B intersect at C, as shown below:. We need to calculate now the value of OD using the Pythagoras Theorem:.

Example 3: Consider two concentric circles of radii 5 cm and 7 cm. A chord AB of the larger circle touches the smaller circle at C. What is the length of AB? Also, C must be the midpoint of AB why? Using the Pythagoras Theorem, we have:.

The "tangent" is derived from the Latin word "tangere", which means "to touch". Sorry for the late response, I lost all comments on my website, just reconstructing now. If Point C only moves in the vertical direction, then it looks like secant would follow the values of the length of the tangent since secant and tangent are both legs of the same triangle.

How can the length of secant approach negative infinity as the lenght of tangent approached positive infinity? Matt, you raise an interesting point. The graphs of secant and tangent do follow closely in the first and third quadrants, where their signs are equal.

It shows nicely how the tangent is rather length expressed as ratio through similarity between the two triangles. A lot can be deduced from that. Thanks a lot! If you plot tangent point one you will find that it is tangent to the circle and intersects: the unit circle, the triangle and the hypotenuse. Where these three intersec is tangent point one.

I have a chart on it that I made that shows this very well , therefore the tangent point is a tangent point on the unit circle. Homophones, Homographs, and Homonyms The same, but different. Ask the Editors 'Everyday' vs. What Is 'Semantic Bleaching'?

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Terms of Use. Discrete Versions of Continuous Functions. Tangent The tangent function is defined by. Mathematica » The 1 tool for creating Demonstrations and anything technical. Contact the MathWorld Team. Family of Curves, Tangents, and Intuition. Recursive Similar Triangles.