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Difference Between Algebra and Trigonometry

Algebra vs. Trigonometry
Both algebra and trigonometry are both math subjects that most high school students are required to study before graduation. These two subjects can also be taught in college level courses, albeit with more rigor. These two math subjects are important to learn and a strong knowledge of both is needed prior to entering into any calculus courses.

Algebra and trigonometry can also have applications in many real world jobs such as construction, engineering and architecture. While learning either subject can be hard for some, there are many resources available to help; tutors and online math assistance are two that come to mind.
Algebra is the study of rules, equations and polynomials in math. The goal is to manipulate numbers and variables to solve a given mathematical equation. There are various forms of algebra which can be studied: elementary algebra, abstract algebra, linear algebra, and even algebraic geometry.

Elementary algebra is the basic introduction to what algebra is, and this is where variables and equation usage are introduced. It is generally taught as a prerequisite for abstract algebra. Abstract algebra is considered higher level math and incorporates sets, commutative properties and associative properties.

Algebra also uses integers, rational numbers, and whole numbers within equations, so these should be learned prior to any algebra instruction. In order to do well in algebra there must be a strong understanding of integers, multiplication, division, as well as addition and subtraction. Typically algebra is introduced before trigonometry in educational systems as it is the basis for other types of math.
Trigonometry is an area of mathematics that deals with triangles and the measurements of sides and angles in triangles. Each angle within a triangle is measured in degrees. In trigonometry, algebra is often incorporated, as the use of variables may be present, so a firm understanding of algebra is recommended before embarking upon a study of trigonometry.

There are three main equations which are worked with in order to find the sides and angles of any triangle: sine, cosine, and tangent. The sides of each triangle is either called the hypotenuse, adjacent, or opposite, depending on the angle in question. A central tenet of trigonometry is that all angles within a triangle equal 180 degrees.
Algebra and trigonometry are both interrelated subjects within mathematics and an understanding of both areas is necessary for success in any endeavor which requires a mathematical background.
Summary

1. Algebra and trigonometry are subjects in mathematics. Algebra is the study of math with rules, equations and variables. Trigonometry deals with triangles and their measurements.
2. There are two main divisions of algebra: elementary and abstract, and both are preparation for calculus courses.
3. Trigonometry uses sine, cosine, and tangent to solve equations. Algebra teaches sets, commutative properties, and associative properties.
4. Both algebra and trigonometry are involved in many real world situations and careers such as engineering, construction and architecture.


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