WHY IS IT USEFUL FOR US TO KNOW TRIGONOMETRY?
 
The true answer is that trigonometry is part of our culture, and should be as visible in daily life as anything in Dickens 
 
or Shakespeare. Why can we not make it so? Why is our daily vocabulary so poor that while we can speak of 
 
Communism, or the national debt, no newspaper ever prints an algebraic formula and no columnist has ever been 
 
known to mention the secant (a function and defined as the ratio of the hypotenuse of a right triangle with respect to an 
 
acute angle of the triangle to the adjacent leg of a right triangle with respect to the same angle) of the angle of 
 
inclination? These things are within our power, and would increase our ability to describe the world and make 
 
reference to its properties quite as much as does our ability to quote Mr. Bumble's or Hamlet.
 
 
 
Trigonometry is part of the equipment of an educated person, as much as history, literature, biology and the rest. We 
 
would even see the world a little differently. Students usually don't ask what good Shakespeare is, or the story of the 
 
American Civil War, or Hitler. References to such things pervade everything we read, or see in the movies, or hear our 
 
relatives talking about, from early childhood; and so we -- as children -- simply understand that knowing about them is 
 
like knowing how to speak and read and write at all. Similarly, children tend to know the necessity of counting change 
 
when making a purchase with a five dollar bill, and counting in general, since they see it around them every day, just as 
 
they see people speaking English.
 
 
 
We would even see the world a little differently. One who has learned trigonometry walks a little taller as a result. Like 
 
any other part of mathematics, or literature, or history, trigonometry furnishes the mind with frameworks that render the 
 
experienced universe more understandable, every day.
 
 
 
How can we present it otherwise, then? Merely telling the kids they will walk a little taller won't do the job. (It might even 
 
be called HIGHTISM.)The subject itself has somehow to be presented in such a way as to convey the lesson of its 
 
own interest. Just as an athlete told to exercise only needs to know his body feels better and stronger as a result, 
 
without necessarily testing the results of each day's exercise by counting his score that day on the golf course, the 
 
intellectual exerciser should get his exercise in a way that makes him feel mentally stronger and happier. If the 
 
exercise is given without context it will usually fail. In the past, with most people, it has failed.

"Why do we learn Trigonometry?"

Trigonometry is easy to defend! Any physical situation where two actors don't meet at right angles or are parallel 
 
requires trig. This includes virtually any realistic mechanics problem (cars on hills, the trajectory of a baseball or rocket, 
 
bridge design, road design, TV picture tube design, etc.) and many optics problems...Taken a step further, 
 
understanding many kinds of motion and vibration (sound, light "waves,"...)Now, try defending integration by parts...
 
  - Tim Corica, The Peddie School
 
 
 
 

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