Why Study Math? Trigonometry and Sohcahtoa

Beginning with "S," oh that's the Sine,

Opposite next, to keep you in line,

Solve A Fraction Problem

Hypotenuse follows, and then you will know,

Opposite over Hypotenuse equals Sine there you go.

Cosine will ensue the "C" gives the clue,

Next is Adjacent, followed by Hypotenuse too,

Now you are rolling and having some fun,

Adjacent over Hypotenuse, the Cosine is won.

Then onto the "T" the Tangent we face,

Opposite and Adjacent finish the race,

It's clear now, you have the key to the throne,

Opposite over Adjacent, the Tangent we own.

Let no man deceive you, let none blind your path,

To this strangeness Chief who teaches you math,

Many have hearkened his voice to hear clear,

And master their trig, year after year.

-From the poem "Chief Sohcahtoa" from the collection Poems for the Mathematically Insecure

Trigonometry is that challenging field of mathematics that deals with the measurements and relationships of the assorted triangles and their sides and angles. It would appear hard to fantasize that so seemingly unglamorous a discipline as this would find itself intertwined in so many corporeal applications of the world around us and in many branches of physics and upper mathematics. Yet this is positively the case.

Trigonometry specifically deals with the estimation of the sides of triangles using extra ratios. Right triangle trigonometry, as the name implies, deals with the estimation of the sides of right triangles using the ratios of sine, cosine, and tangent. These three mathematical entities are nothing more than easy ratios as expressed by the sides of a right triangle. If you recall from your basic geometry days, a right triangle has one angle whose quantum is 90 degrees. The side opposite the right angle is called the hypotenuse and the other two sides, legs.

The manner in which we guess the sine, cosine, and tangent of any right triangle is to use ratios based on the sides of the right triangle. Mathematicians have come up with a challenging mnemonic to remember these formulas, and if you have already read Poems for the Mathematically Insecure, then you know from Chief Sohcahtoa the way to do it. That is, the sine is equal to the distance of the opposite side to the distance of the hypotenuse; the cosine, the adjacent to the hypotenuse; and the tangent, the opposite to the adjacent.

Once we know these formulas, we can put these ratios into all sorts of uses. For example, the sine and cosine can give us the resultant force when doing leg presses in our local gym. The tangent can tell us the height of a building when we know how far we are standing from it. These ratios can also tell us how to ease the endeavor required by a man belaying a rock wall climber.

Not too bad for three easy ratios! What is even more challenging is that higher up in mathematics we see these challenging creatures popping up all over the place to help aid us in solving a myriad of mathematical problems. So go meet Chief Sohcahtoa and these three trigonometric ratios. You too will then be able to use them in some everyday ways.

See more at Cool Math Ebooks and come meet Chief Sohcahtoa here Cool Math Poems Ebook

Why Study Math? Trigonometry and Sohcahtoa