Both Trigonometry and geometry are two associated branches of mathematics. Geometry deals with the study of different shapes, their characteristics, features and their mathematical aspects. Trigonometry on the other hand is associated with one of such shapes studied in geometry. Trigonometry deals with the study of triangles and their properties. It encompasses various formulae and techniques to solve complex problems associated with triangles and other figures that can be fragmented somehow into triangles. If you are a student and looking for your Geometry Homework Help, this article will help you in making your assignment.
Students who are newly introduced to these concepts often get confused and cannot figure out the utility of trigonometry. Since geometry already deals with some basic aspects of triangles, students are bound to question the need for trigonometry. However trigonometry, which is an established field of study and teaches how to deal with more complicated phenomena associated with triangles has its own advantages, which shall be discussed in this article. This article provides an insight into the key differences between trigonometry and geometry.
GEOMETRY
In mathematics, geometry is a defined branch of study that deals with points, lines, line segments, rays, arrows, angles and finally shapes. It teaches how to measure and construct figures. It also allows students to accomplish problems associated with measurement, construction, angles and shapes. Through geometry students get to know about the angular aspects of things like the right angles, straight angles, a 360 degree and they get to see things from a fresh perspective. It is classified into the study of figures in two and three dimensional planes. The study of geometry also comes handy while pursuing higher studies in engineering or mathematical streams.
FEATURES OF GEOMETRY
Here are some of the distinguishing features of geometry that can help students get a clear idea of geometry. After learning about these features students can easily describe what geometry is and what are its key features and applications.
- Measurement: Geometry deals with the measurement of shapes. It also attempts to establish a logical relationship between these shapes. It introduces students with the problems related to calculation of areas and perimeters of shapes at the primary level.
- Geometrical properties: Geometry strives to expose students to the mathematical properties of shapes and figures. It also familiarizes students with non conventional and new figures that hitherto went unnoticed by them.
- Base for further studies: Geometry establishes the necessary base for the study of higher and more complicated concepts in mathematics. Trigonometry is one such concept and requires prior knowledge of geometry.
- Applications: Geometry has a wider set of applications and its concepts apply to interior designing, calculation of interstellar distances, computer graphic designing etc.
WHY STUDY GEOMETRY?
- It facilitates the study of advanced concepts in measurement.
- Geometry applies to the field of graphic designing.
- It forms the foundation for the study of trigonometry.
- It is helpful in the field of interior design.
- Geometry is also vital in the field of art.
TRIGONOMETRY
Trigonometry happens to be a subset of geometry and deals solely with triangles. It is mostly associated with the sides of triangles. It uses trigonometric ratios to find out the sides and areas of triangles and figures that can be fragmented into several triangles. The six trigonometric ratios used for this purpose are sine, cosine, tangent, cotangent, secant and cosecant. These ratios apply to the right angled triangles according to their respective sides (Height, Base, Hypotenuse) based on their angular positions.
FEATURES OF TRIGONOMETRY
Trigonometry can be studied first at elemental and then advanced level. In the initial phase it deals with the finding of sides and areas of right angled triangles. Later in the advanced phase it deals with more complex phenomena. Here are some of the distinguishing features of trigonometry.
- Triangles: Trigonometry solely deals with triangles, and in that more closely with the right angled triangles. All its ratios are based on the properties of a right angled triangle.
- Trigonometric formulas and tables: Trigonometric formulas are derived from the above mentioned six fundamental trigonometric functions. It is through these basic functions that more complicated trigonometric equations are evolved at the advanced stages.
- Applications: Trigonometry has an elemental role in the designing and construction of large infrastructure projects. It is a vital component of architectural studies. Trigonometry specially segregates from geometry owing to this substantial set of applications.
WHY STUDY TRIGONOMETRY?
- Study of trigonometry facilitates solving complex mathematical problems.
- Trigonometry is vital in the construction designs.
- It is elemental in oceanography.
- It forms the basis of calculus in mathematics.
- Knowledge of trigonometry is required to pursue higher education in the engineering sector.
CONCLUSION: Geometry vs. Trigonometry
Both geometry and trigonometry are distinct fields of study that play significant roles in different areas of work. Geometry introduces students to the study of shapes and their mathematical properties, while trigonometry deals with the properties of triangles and problems associated with it.
Having their applications in diverse fields both the distinct fields of study are vital components of the mathematics curriculum. After reading this article students must get a clear idea about the features, applications and utility of both geometry and trigonometry.