Jordan's inequality states that for

Prove Jordan's Inequality.

Discussion:

What does this inequality say? We have a curve, y = sin x, placed between two linear functions in the range . The inequality is reversed in the range . One interpretation of this is that in this range, the value of sin x is always less than the curve tangent to the sine curce at the origin (y = x) and it always lies above the chord of the sine curve between the origin and .

So what? Why is the Jordan Inequality important in pure or applied mathematics?

Who was

Jordan?

HINTS for thinking about a proof:

Consider a unit circle, OA = 1 with a point P on the circle. Construct a perpendicular from P to the x-axis with M being the foot of the perpendicular and Q its reflection in the x-axis. Let x be the measure of the angle POM. The line PM has length sin x.

Construct a circle of radius MP and center at M.

Find elements in the figure that reflect what you are to prove in Jordan's Inequality.

Reference: Yuefeng, Feng. (1996) Proof without words.

Mathematics Magazine. 69,p. 126.

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