What is trigonometry?

What is trigonometry? The word trigonometry comes from two Greek words. These two words are trigonon (triangle) and metria (measure). Therefore, trigonometry is a branch of mathematics but especially a branch of geometry, that specializes in the measurement of triangles.

Definition of the trigonometric functions

Suppose you have a right-angled triangle such as the one you see below. Notice that the hypotenuse is the longest side of the triangle.

There are six basic trigonometric functions that are commonly used to solve problems. These are sine function, cosine function, tangent function, cotangent function, secant function, and cosecant function.

• sine θ = sin θ = Opposite / Hypotenuse

• cosine θ = cos θ = Adjacent / Hypotenuse

• tangent θ = tan θ = Opposite / Adjacent

• cotangent θ = cot θ = 1 / tan θ =  Adjacent / Opposite

• secant θ = sec θ = 1 / cos θ = Hypotenuse / Adjacent

• cosecant θ = csc θ = 1 / sin θ = Hypotenuse / Opposite 

To help students remember the formulas for sin θ, cos θ, and tan θ, teachers usually use the following acronyms:

soh: sineoppositehypotenuse

cah:cosineadjacenthypotenuse

toa:tangentoppositeadjacent

Delve deeper with these trigonometry lessons

Additional topics in trigonometry

Who invented trigonometry?

Astronomers use trigonometry a lot to calculate distances and positions of planets. Hipparchus of Nicaea, often considered the greatest astronomer of antiquity, is the one who invented trigonometry according to many scholars.

Trigonometry has been around for more than 3000 years. The Babylonians, the Greeks, and the Egyptians all used trigonometry to find the lengths of the sides of triangles and the measures of their angles. About 3000 years ago, trigonometry was used in astronomy and surveying among a few others. 

Greek astronomers such Hipparchus, Copernicus, and Ptolemy made some valuable contribution to astronomy. However, the small success that the heliocentric hypothesis (the sun is at the center of the solar system) experienced was mainly due Hipparchus. Hipparchus was also the first one to come with the a table of chords which were the earliest examples of trigonometric values.

What is trigonometry used for? Here are some applications of trigonometry

The fields that trigonometry is being used for today include electronics, engineering, calculus and satellite navigation systems.

Trigonometry has also expanded to include a vast number of physical phenomena including sound waves, light rays, pendulums, and orbits of atomic particles.

A study of trigonometry will primarily involve concepts of angles, the right triangle, and the unit circle.

The problems you can solve with trigonometry are many. A short list includes the following:

• Angle of elevation

• Angle of depression

• Height of a very tall building

• Diameter of the moon

• The area that is swept clean by a windshield wiper

My goal is to help you understand and master trigonometry in no time and with no tears.

I have designed the lessons carefully backed up with years of experience teaching mathematics in high school.

I have organized the lessons to follow a logical pattern. Therefore, study them in the order shown above.

I am confident you will conquer trigonometry when you reached the end. Lessons will be added on a regular basis, so come back here often to see if a new lesson was added.

When is trigonometry taught?

When you take a geometry class in the 10th grade, the teacher may cover some basic concepts in trigonometry. However, a complete study of trigonometry will require an entire school year. Trigonometry makes use of many important concepts in algebra and geometry. That is the reason algebra and geometry are prerequisites. 

In general, trigonometry is taught after you have completed courses in pre-algebra, algebra, and geometry. In the United States of America, trigonometry is usually taught in the 11th grade.

Students do not always have to pick trigonometry though. If they are gifted, they could also take pre-calculus in the 11th grade. A Pre-calculus textbook usually has some sections that cover trigonometry extensively. Students could also take a combination course called algebra and trigonometry in the 11th or 12th grade. 

It is not common to take trigonometry in middle school unless a student is dedicated, gifted or a prodigy.