for all you mathmaticians !?

Question

A tunnel connects two points A and B on the earth's surface as shown at the right. the surface distance from A to B is 200mi. Use two terms of the power series for cosx to approximate the maxiumum depth of the tunnel. use the approximation 2000 mi for the radius of the earth

Answer 1

d = 2,000(1 - cos(100/2,000)
d = 2,000(1 - cos(0.05))
d = 2,000(1 - (1 - (1/2)(0.05)^2)
d ≈ 2,000(1/2)(0.0025)
d ≈ 2.5 miles