Mathematics: When two railroad tracks merge, the overlapping portions of the tracks are in the shape of a circular arc. The radius of each are r in feet and the angle theta are related by (x/2) = 2r(sin(theta/2)2. write a formula for x in terms of cos theta

When two railroad tracks merge, the overlapping portions

oddoneshenchman

20.01.2022

$x=2r(1-cos \theta)$

Step-by-step explanation:

Given equation,

$\frac{x}{2}=2r(\sin(\frac{\theta}{2}))^2$

$\frac{x}{2}=2r\sin^2(\frac{\theta}{2})$ ...... (1)

Since,

$\cos 2A=1-2\sin^2 A$

$\implies 2\sin^2A = 1 - \cos 2A$

Thus,

$2 \sin^2(\frac{\theta}{2})=1-\cos \theta$ ...... (2)

From equation (1) and (2),

$\frac{x}{2}=r(1-\cos \theta)$

$x=2r(1-\cos \theta)$

Which is the required formula.

0,0(0 оценок)