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.
Explore our full library of trigonometry courses:
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 real-world 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 Lessons and Skills
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 real-world situations and word problems. Here, students can prepare by mastering word problems covering the Pythagorean Theorem, special triangles, identities, and real-world situations involving trigonometric equations.
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