(a) The accompanying figure shows a sector of radiusr andcentral angle 2. Assuming that

Chapter 9, Problem 40

(choose chapter or problem)

(a) The accompanying figure shows a sector of radius \(r\) and central angle \(2 \alpha\). Assuming that the angle α is small, use the local quadratic approximation of \(\cos \alpha\) at \(\alpha=0\) to show that \(x \approx r \alpha^{2} / 2\).

(b) Assuming that the Earth is a sphere of radius 4000 mi, use the result in part (a) to approximate the maximum amount by which a 100 mi arc along the equator will diverge from its chord.

Equation Transcription:

Text Transcription:

r

2 alpha

cos alpha

alpha=0

x almost = r alpha^2/2