Tuesday, April 17, 2007

Luis DP's Answer to JBarrika

Dear JBarrika,

Your question is: What are trigonometric functions like sine, cosine, tangent, and the inverses really useful for?

Trigonometry is essential for the human knowledge of space. Trigonometry has applications in almost all natural and social sciences. Engineering, physics, astronomy would be in huge trouble without the existence trigonometry or trigonometric functions. Let me give you an example. As you may have noticed before, curves in roads or highways are slightly slanted in the direction in which they are concave down. Civil engineers determine this slant angle depending on the acuteness of the curve. The sharper the curve, the greater will be the angle formed by the horizontal and the road. This is a complex trigonometric relationship that civil engineers take into account during road and highway construction. This slant angle generates a horizontal component of the normal force that counteracts the centrifugal force. As you may have noticed, many roads in Colombia lack a significant slant angle, making vehicles traveling at high speeds vulnerable to fly out of the road in the direction in which the curve is convex up.

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