Geometry Vs Trigonometry: ELI5 The Difference

Mathematics is full of wonders. You learn so many things as you delve deeper into mathematics that it will leave you hungry for more. Mathematics consists of different topics like arithmetic, algebra, geometry, trigonometry, mensuration, etc. Among these sections, people might often get confused between trigonometry and geometry.

But, these two- geometry and trigonometry- are not alike. Instead, they have quite a few differences between them. In the following, we will explore geometry and trigonometry and how they differ. So, let’s first know these two in simple terms.

What is geometry?

Geometry is all about various shapes. Looking around, you will find that different things are different shapes. For example, your book and your pencil are not of the same shape. Your book is either square or rectangular. But your pencil is cylindrical. When you draw a dot on a page, it is a ‘point,’ and you use some straight lines when you draw a house. So, geometry considers all these shapes and studies them.

What is trigonometry?

Trigonometry is all about triangles. If you do not know what a triangle is, let us give an example to you. A slice of pizza is triangular. You must have seen the traffic cones on the road, haven’t you? That structure is triangular. So, trigonometry measures the angles and sides of a triangle, especially a right-angle triangle. Here is an example to help you understand what a right angle is. When the clock strikes three, the hands make a right angle.

The above information is the basic knowledge about the two terms geometry and trigonometry. Now, let’s move on to exploring the differences.

Major Differences

Though both concepts deal with shapes, there are quite a few differences between geometry and trigonometry. Check them out in the following points.

1. Area of study

Geometry is concerned with shapes, lines, planes, and points. It focuses on exploring the relationship among various shapes. You can measure all possible shapes by using geometry and its theories.

Trigonometry, on the other hand, deals with triangles only. Even in situations where there are only two lines and one angle (for a triangle, you need three lines and three angles), trigonometry takes the help of imaginary lines to draw a triangle and solves the problem.

2. Study of properties

Geometry studies the properties of all types of geometrical figures. Be it a simple structure like a line or a complex structure like a hexagon- geometry covers everything. Properties of triangles of different types, like right-angle, equilateral, acute, obtuse, etc., are all included within the geometry’s scope.

But, trigonometry does not concern any geometrical shapes other than a triangle. To be more specific, trigonometry studies the properties of a right-angle triangle. If you are thinking of learning what a circle is, you have to find it in geometry. But, if you are thinking of calculating how high the lamp post on the road corner is, you have to learn trigonometry.

3. Branch of mathematics

Geometry is the direct branch of mathematics covering geometric calculations, theories, and formulas. So, without knowing mathematics properly, you will not be able to ace geometry.

Trigonometry is also a part of mathematics. But, trigonometry is derived from geometry only. As we told you in the previous point, all triangles are geometric shapes, just like everything else. But, trigonometry concerns the triangle only. So, if there were no triangles in geometry, trigonometry would not be able to explore them. Thus, we can call trigonometry a subset of geometry. Similarly, geometry is the superset of trigonometry.

4. Study of angles

Suppose you spill some water on the floor. Now you have a splatter of water. If you wonder how much area the water has covered, you have to do some complex math with geometric calculations. You have to measure the length and width of each water stain and then calculate the total. In this measurement process, you take the help of angles and sides. Thus, geometry is about studying the properties of angles and calculating their sums.

Trigonometry focuses more on the measurement of angles. Let’s take the example of the lamp post again. To measure its height using trigonometry, you need to find the angle, its shadow is making with the road. Thus, when it comes to angles, trigonometry deals with the measurements only.

5. Categories

Geometry has three broad categories. These are plane geometry, spherical geometry, and solid geometry. We told you earlier that any shape is under geometric concern. Now, there are a lot of various shapes. So, it becomes difficult to gauge them all if you do not classify them.

• Any shape similar to a circle or sphere is under spherical geometry.
• Shapes existing on a flat surface (like a piece of paper) are included in the plane geometry.
• The three-dimensional shapes (like the boxes you get from Amazon, the ball you play with, etc.) are under solid geometry.

Trigonometry is broadly categorized into four categories. These are core, analytic, spherical, and plane.

• In core trigonometry, you study only right-angle triangles by using two things- sine and cosine. Mathematicians mostly use this category.
• You use plane trigonometry when you find the height and distances of angles of a plane triangle. If you become a mechanical engineer, a physicist, an architect, or a chemist, you will use trigonometry extensively.
• Spherical trigonometry measures triangles on a sphere. For example, the earth is a sphere. This trigonometry is of great use to astronomers, mapmakers, navigators, etc.
• Analytic trigonometry is just another part of core trigonometry. Both scientists and engineers use this.

6. Terminologies used

Trigonometry uses some specific terms. These are unique, and you do not find them in any other part of mathematics. There are six such terms or ratios used here. These are sin, cosine, tan, cot, sec, and cosec.

Geometry has some specific terminologies also, but those are not as unique as trigonometry. Some common geometric terms are straight angle, right angle, line, point, ray, etc. However, you will find these words in other areas also. Thus, concerning the terms used, geometry and trigonometry differ.

7. History

Both geometry and trigonometry have their origin in Greece. But both were not introduced by a single person. Euclid was a great Greek mathematician. We call him the ‘Father of Geometry.’ As for trigonometry, we have another Greek mathematician named Hipparchus. These scholars first used geometry and trigonometry years ago. In 3000 BC, we find geometric records. Trigonometry is comparatively more recent, starting from 190 BC.

8. Grade in school when you learn geometry and trigonometry

In elementary and middle school, you learn almost all aspects of mathematics in small parts. But, when you reach high school, your grades determine which math course you will take. It takes till ninth grade to read and learn core geometry. In this grade, the teachers teach about parallel lines, the Pythagorean theorem, etc.

In junior year, your course contents might already have trigonometry included. After passing ninth and tenth grade with geometry in high school, you get Algebra II. Here you learn about basic and advanced identities and theories of trigonometry.

9. Uses in real life

Geometry and trigonometry have extensive uses in our daily lives. From constructing a house to drawing a piece of art, geometric and trigonometric knowledge play essential roles. Geometry is used in developing video games, designing robots, building structures like monuments, and sports like soccer, badminton, cricket, baseball, etc. For example, the shape and area of a cricket bat determine how hard and far it can hit a ball to add scores on the board.

Trigonometry is also used in our daily lives, but not in all the sectors where geometry finds its use. You must have seen how NASA launches rockets and spaceships into space. They determine the location of launching these by using trigonometry. When you play Mario, you actually see the outcome of a trigonometric calculation on screen. If we ask you the height of the tallest mountain in the world, we know you will have your answer ready and say it is Mount Everest. Experts measured it by trigonometry only. Thus, trigonometry is used in various real-life situations.

Other differences between geometry and trigonometry include: Pythagoras’ theorem is essential in trigonometry, and most trigonometric measurements are based on this theorem. However, geometry includes using various other theorems and formulas besides the Pythagorean theorem.

Summing up

Here is a tabular presentation of the differences we mentioned above:

Wrapping up

To sum up, everything we have mentioned above concludes that trigonometry is the wing of mathematics where triangles, specifically right-angle triangles, are studied. In contrast, geometry is about exploring the properties of all geometric shapes. In mathematics, both are important. When you put mathematics into real-life situations, you will see that you need to implement both at various levels. Despite their differences, geometry and trigonometry are integrally associated.

Manpreet Singh

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having  just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,