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Physics LibreTexts

19.2: Tangent to the Cycloid

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The slope of the tangent to the cycloid at P is dy/dx, which is equal to dy/d\theta , and these can be obtained from Equations 19.1.1 and 19.1.2.

Exercise \PageIndex{1}

Show that the slope of the tangent at P is tan \theta . That is to say, the tangent at P makes an angle \theta with the horizontal.

Having done that, now consider the following:

Let A be the lowest point of the circle. The angle \psi that AP makes with the horizontal is given by \tan \psi = \frac{y}{x - 2 a \theta }

Exercise \PageIndex{2}

Show that \psi = \theta . Therefore the line AP is the tangent to the cycloid at P; or the tangent at P is the line AP.


This page titled 19.2: Tangent to the Cycloid is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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