Trigonometry: Formulas, Analytics, Ratios & Basics
FOR TEACHERS AND PARENTS
What is Trigonometry?
Trigonometry is the study of how the sides and angles of triangles relate to each other. At first glance, this may seem like a rather limited field, but it is, in reality, an entire branch of mathematics. Triangles can be used to describe any polygon or circle, and the relationships between the sides and angles of triangles define important concepts in geometry, calculus, and beyond. Learning to construct and analyze triangles requires a solid foundation in mathematical logic and reasoning.
A study of trigonometry begins by understanding the basics of triangles and their geometry, like how to identify the different types of triangles and how side lengths are important to their construction. This leads to more sophisticated activities, such as learning to complete the description of a triangle from incomplete information and using logic and trigonometry rules to prove various trigonometric identities using sine, cosine, tangent, cosecant, secant, and cotangent. Eventually, one can take trigonometry all the way into calculus and linear algebra.
Trigonometry has a host of realworld applications in design, statistics, and many other fields. Physicists understand ballistics and vectors through trigonometry. Computer graphics are built of polygons on top of polygons, all of which can be broken down fundamentally into groups of triangles. Triangles and their ratios frequently find their way into fields like construction, surveying, and geography, where they sometimes simply make things easier and sometimes are essential for a job. Trigonometry forms part of the mathematical foundation that all students build as they grow and learn.
Trigonometry Topics
Angle measure
Learn about how to find the measure of an angle. Discover how to estimate an angle using commonly understood degrees and how to measure an angle with a protractor.
Applications of trigonometry
Explore trigonometry applications. Learn about what trigonometry is used for and its reallife applications by reviewing examples and their importance.
Practical Applications of Angles
Explore the practical applications of angles in real life. Find out what an angle is and understand its different types. Discover reallife examples of angles.
Right triangles
What is a right triangle? Learn its definition and properties. See the Pythagorean Theorem and the Right Triangle Altitude Theorem, and use them in proofs.
Trigonometric functions
What are trigonometric functions? Learn more about all 6 trig functions, which formulas to use and examples of how to solve different trigonometric problems.
Trigonometric identities
Learn to define basic trigonometric identities. Discover the doubleangle, halfangle, and other identities. Learn how to use trigonometric identities. See examples.
Types of angles
What are the different types of angles? Learn about acute, right, obtuse, and straight angles and find out what each of the different kinds of angles look like.
Trigonometry Resources
As trigonometry has so many applications, there are a variety of resources on the subject at several different grade levels. Students can find course pages dealing directly with trigonometry as well as individual trigonometry lessons that are part of other math courses or fields of study. Study.com offers tutoring solutions and test prep for many different standardized tests so that students of many different experience levels can find their way through the study of trigonometry.
Trigonometry Courses
The wealth of trigonometry lessons here means that trigonometry appears in many different fields of study. At the same time, courses dealing directly with trigonometry are readily available. Depending on their age, learning goals, and experience level, students can deal with only the trigonometry applications they need to, or they can follow it wherever it leads. There are courses for trigonometry as it relates to algebra, geometry, and calculus, as well as test prep for different standardized tests. Students should find all of the resources they need for personalized study right here.
Trigonometry Skills and Practice
Trigonometry skills practice can be used to solidify skills in trigonometry, basic math, and higher mathematics, and also to understand the relationship between them all. Students can work with algebra and geometry skills, such as polynomials, understanding how triangles relate to other shapes, learning different types of functions, understanding the domain and range of a function. They can also practice graphing, translating, rotating, and transforming functions. Working directly within trigonometry, students can master measuring angles in both degrees and radians, constructing and working within the unit circle, and using trigonometric ratios.
Progressing along, students can practice using special triangles, graphing trigonometry functions on the coordinate plane, Pythagorean identities, and analytic trigonometry. Further courses provide practice in dealing with trigonometric equations and identities and how to apply them, solve them, and prove them. For more complicated aspects and applications of trigonometry, skills practice is offered concerning vectors, polar coordinates, dot products, and conic sections.
Practicing skills in trigonometry is excellent preparation for many other fields of study, and it is good practice for mathematics in general. These skills can be used in basic trigonometry, AP trigonometry, all the way to college trig, and they will serve students on their way to using trigonometry to solve integrals in calculus. Much like the other large branches of math, such as algebra and geometry, trigonometry offers applications in fields that may not seem related at a first glance, from manual labor to medicine to academia.
Standardized tests, including the SAT and ACT tests, frequently lean on students' knowledge of trigonometry. Individual states often have their own standardized tests, like the Florida Math Standards (BEST) test, for which preparation resources can be found on Study.com. The BEST test, in particular, is a comprehensive survey of high school trigonometry. Skills practice lessons include the six trigonometric ratios, right triangles, the coordinate plane, and working with both degrees and radians. Students can also practice with or without a calculator. The Florida Math Standards Test tests practical math skills extensively, using realworld situations and word problems. Here, students can prepare by mastering word problems covering the Pythagorean Theorem, special triangles, identities, and realworld situations involving trigonometric equations.
Trigonometry Homeschool Curriculum
Homeschool courses on Study.com are short lessons that can be tackled on a flexible schedule at a student's own pace. Students can pick up their trigonometry lessons as part of High School Algebra II: Homeschool Curriculum for the basics, or go straight into High School Trigonometry: Homeschool Curriculum to go head on into trigonometry studies. Video lessons help students on their way to mastering trigonometry. Multiple choice quizzes allow them to test their progress as they move along.
Homeschool solutionsStudy.com is an excellent program that can help my children learn anything. The incredible library of videos is more than I could have ever hoped for.
Frequently Asked Questions

What is trigonometry with an example?
Trigonometry is the study of how the sides and angles of triangles relate to each other. Within triangles (especially right triangles), the ratio of the three sides to each other forms a predictable pattern that can be described with the trigonometric ratios sine, cosine, and tangent. Triangles can also be used to describe larger, more complicated polygons, as well as circles.

What are the basics of trigonometry?
The basics of trigonometry include the fundamental rules of triangles, such as the sum of the interior angles, and the different types of triangles. Angles are also crucial to basic trig, so an understanding of how to draw and measure angles is important. Properties of right triangles and the trigonometric ratios are needed for a basic understanding of trig.
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