Trigonometry is the mathematical study of length, sides, and angles, and their relationship in a triangle. Its name literally means “triangle measure”.
Despite what some students believe, trigonometry is useful in a slew of different disciplines, such as astronomy, geography, physics, engineering, oceanography, architecture, digital imaging, and many other areas that involve measurement problems.
Not only that, but as a student, learning about trigonometry helps you understand the natural order of things and some physical phenomenons around you. It also strengthens your mathematical thinking, which is a powerful cognitive process that allows you to solve some of the problems that occur in science or in your everyday life.
If you’re an 8th or 9th grader, it’s likely that you’ve come across trigonometry already (or will do very soon). In either case, you should become familiar with some basic trigonometry concepts if you want to learn it effectively. To help you out in this department, below you’ll find a glossary explaining the most common trigonometry terms, so you can study them and get a head start on this crucial mathematics course.

Basic Trigonometry Dictionary

Angle

The angle refers to the measurement of rotation, or the amount of space between two intersecting lines. There can be angles of elevation, of depression, quadrantal angles, among others.

Vector

It is a mathematical structure in a frame of reference that represents both magnitude and direction. In trigonometry, there are component vectors, algebraic vectors, geometric vectors, equivalent vectors, and more.

Trigonometric Function

A trigonometric function refers to the function of an angle which establishes the relationship between the length and angles of two sides of a right-angled triangle. There are six trigonometric functions (which will be explained later on in this post): sine, cosine, secant, cosecant, tangent, and cotangent.

Inverse Function

As the name implies, an inverse function comes to be when the variable outputs of a function are expressed as the inputs of another function. Arcsine, arccosine, and arctangent are all inverse functions.

Period

In trigonometric terms, the period expresses how many times the smallest value in a periodic function repeats itself. A periodic function is a trigonometric function whose values regularly repeat themselves (once each period).

Hypotenuse

When studying a right triangle, the hypotenuse will be its longest side. It can also be defined as the side that’s opposite to the right angle in the triangle. You can workout the length of the hypotenuse with the Pythagorean Theorem (a^2+b^2=c^2) if you know the length of the 2 catheti of the triangle.

Cathetus

As some of the other terms in this dictionary, this one is pertinent to geometry, but you should still know it to understand trigonometry. The cathetus (plural: catheti) refers to an adjacent side to a right angle. In a right triangle, the longest side is the hypotenuse, and the two other shorter ones are the catheti. You can differentiate the catheti as adjacent or opposite. The adjacent is the one that forms the angle you're interested in along with the hypotenuse. The opposite cathetus is the side that's directly in front of the angle you're interested in.
If you’re having a challenging time fully understanding the definitions in this glossary, don’t worry. The Tutoring Center, Katy TX offers an “Advanced Placement Math Program” which goes over high-level math courses, such as pre-calculus, algebra, and trigonometry. Contact them at 832-437-0635 for math tutoring classes in Katy TX, or to request a free consultation.

Asymptotes

In trigonometric functions, asymptotes are lines that represent undefined values.

Trigonometric Identity

As far as trigonometric identities go, they are equations formed with trigonometric functions that are true for all of the values of that angle.

Cosecant

The cosecant is the complementary trigonometric function of sine, and represents the ratio of the hypotenuse and the opposite cathetus of a right triangle. It is abbreviated as csc or cosec.

Cosine

The cosine is the ratio of the adjacent cathetus to the hypotenuse in a right triangle. It is abbreviated as cos.

Cotangent

The cotangent is the complementary trigonometric function of tangent and expresses the ratio of the adjacent and opposite catheti. It is abbreviated as cot, cta, or cotg.

Secant

The secant is the complementary trigonometric function of cosine and expresses the ratio of the adjacent cathetus to the hypotenuse. It is abbreviated as sec.

Sine

The sine expresses the ratio between the opposite cathetus and the hypotenuse. It is abbreviated as sen or sin.

Tangent

Finally, there’s the tangent, which is the ratio between the two catheti of a right-angled triangle. It is abbreviated as tan or tg.

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