What is the difference between the geometric secant(the line that cuts two points of a curve) of a curve, and the trigonometric secant(=1/cosinex) ? If they are the same, can you explain how they are the same?
Could you please explain, I am not able to see it intuitively.
Thank you!
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$\begingroup$"Secant" means it cuts the curve. It doesn't have to cut in exactly two points. It could cut the curve three times, or just once.
That said, the trigonometric functions such as tangent and secant describe finite lengths, whereas the geometric tangent and secant are lines of infinite length. There is barely any connection between the two uses of the terms.
If you are likely to get the trigonometric secant mixed up with the tangent, you can recall that when we draw them on a unit circle the tangent is tangent to the circle and the secant cuts across the circle. But I wouldn't look for any connection more meaningful than that.
$\endgroup$ $\begingroup$Let me Google that for you: (see the diagrams to the right)
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