When math students hear the word “Trigonometry,” it often leads the uninitiated shaking in their boots. We only need to take a quick look at where the word came from, though, to see that it isn’t as terrifying as many students think. Its origins lie in the Greek words for triangle (trigonon) and measure (metron). So, simply put, trigonometry is just the study of measuring triangles. It would be hard to learn everything there is to know about trigonometry in just one post, but taking a look at some common terms and equations can certainly help students start forming a basis of essential knowledge.
Equilateral, Isosceles, and Scalene Triangles
All triangles have three sides and three angles. However, not all triangles are equal; in fact, only equilateral triangles are equal! Every equilateral triangle, regardless of size, has three sides that are the same length and three angles that are always equal to 60o. On the other end of the spectrum are scalene triangles, which have no equal sides or angles. Isosceles triangles form the middle ground between these two extremes with two equal sides and two equal angles.
Acute, Right, and Obtuse Triangles
This set of terms helps us describe the angles in different types of triangles. An acute triangle has only angles that are less than 90o, right triangle has one angle that is exactly 90o, and an obtuse triangle has one angle that is larger than 90o.
Determining Basic Measurements
The most basic functions of trigonometry are to determine the perimeter and the area of any triangle. Finding the perimeter is very easy and requires only basic addition: simply measure the three sides and add these measurements together. Finding the area is just slightly more complicated. It requires following the formula: Area = ½b x h, in which “b” stands for “base,” and “h” for “height.” This formula can also be written out as A = bh/2. Choose any side for the base of the triangle, and then measure the height at a right angle to it. Simple, right? Let’s try something harder.
Sine, Cosine, and Tangent
When one side or angle of a triangle is not defined, these three functions can help to determine its value. Put simply, each of these seemingly complex functions is actually just one side of a right triangle being divided by another side. They are defined in relation to a known angle, often defined as “θ,” and can be abbreviated to “sin,” “cos,” and “tan.”
Hypotenuse, Opposite, and Adjacent Sides
The sides of a right triangle are given different names depending on where they sit in relation to the angle “θ,” which can be the angle on either side of the hypotenuse. The hypotenuse is consistent: it is always the longest side of the triangle, and is always located opposite the right angle. The adjacent side is next to the angle “θ,” and the opposite side is across from it.
How Is This Useful?
Now that we know all of these terms and equations, what can we do with them? Trigonometry allows students to take any triangle with three known sides or angles, and fill in all the missing information using the sine, cosign, and tangent functions. Of course, understanding these terms and functions only helps a student form a knowledge base to work from. Advanced trigonometry is much more complex.