(Note that the ratio is not defined when x equals 0)

A. Referring to the figure, show the following:

A sub 1 = area of triangle QAP = (sin x) / (2)

A sub 2 = area of sector OAP = (x) / (2)

A sub 3 = area of triangle OAB = (tan x) / (2)

B. Using the fact that A sub 1 < A sub 2 < A sub 3, which we can see clearly in the figure, show that

cos x < (sin x) / (x) < 1 x > 0

C. From the inequality in part B, explain how you can conclude that for x > 0, (sin x) / x approaches 0.