MHB Some Geometry Some Calculus Some Trigonometry

[Wasif Jalal]

Show that y≈∆φ×secφ in the jpeg attached.

or ∆y = sec φ

A and B are points on curved surface, two lines are extended through origin to a line that is tangent to the circle, these points are A' and B', change in Angle will bring a change in length between A' and B'. I need to know how is this do-able.View attachment 7296[ATTACH=

 

[MarkFL]

Are you sure you don't mean:

$$\Delta y\approx\sec^2(\varphi)\Delta \varphi$$?