Does a trigonometry tangent relate to a circle's tangent?

Answer 1

A circle's tangent is exactly the same as a triangle's tangent. If you look at a circle, you can make the radius the hypotenuse. Then make a vertical line from the point, and a horizontal line from the center. If you look, you have a triangle made inside the circle. This is why angles can be measured in radians, a unit that is derived from the circumference of a circle.

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By doing a little calculus, we find that the slope of the equation of a circle-the slope of the tangent line-is given by the tangent of an angle.

AnswerEverything written above is correct, but doesn't have anything to do with tangents (in the circle sense of the word).

Suppose you're given an angle theta. Draw a circle together with two radii, one horizontal and the other at an angle theta from the first one. (So far, this is the same as above.) Now draw the tangent to the circle at X, the point where the non-horizontal radius meets the circumference. Let Y be the point where this tangent meets the horizontal line through the centre. Then, assuming the radius is 1, tan(theta) is the distance XY, which is the length of part of the tangent.