Free online courseTrigonometry Course

Course Description

The "Trigonometry Course" is an immersive learning experience that spans over a comprehensive 6 hours and 14 minutes. This course, categorized under Basic Studies and more specifically under Trigonometry, provides a detailed and structured exploration of trigonometric principles, making it an essential resource for foundational mathematics education.

The course kicks off with TR-00, providing an engaging "Introduction to the Trigonometry Series." This sets the stage for the subsequent deep dive into the world of angles, beginning with TR-01, which introduces the basic concepts of angles, followed by TR-02 that elaborates on the different types of angles. TR-03 extends this knowledge to explore angle relationships, laying a solid groundwork for the measurements covered in TR-04 and the more advanced nuances of degrees, minutes, and seconds in TR-04Z.

Continuing the journey, the course transitions to radians in TR-05, which introduces the concept of radians, and TR-06 which delves into measuring angles in radians. This is complemented by a review of essential geometric concepts related to triangles in TR-07, including the first proof of Thales' Theorem in TR-07Z. The significance of triangles is further emphasized in TR-08, discussing similar and congruent triangles, followed by an exploration of the Pythagorean Theorem in TR-09 and its proof in TR-09Z. TR-10 introduces Pythagorean triples, enhancing the relationships between different types of triangles.

The course meticulously covers the distances between points, both in a plane (TR-11) and in space (TR-12), before introducing the core trigonometric ratios in TR-13, and the origins of co-trigonometric functions in TR-13Z. The unit circle, a fundamental concept in trigonometry, is covered in TR-14, followed by practical applications of sine and cosine values in common angles (TR-15) and their proofs (TR-15Z).

From using a calculator for trigonometric functions in TR-16 to exploring the most common uses of trigonometry in TR-17, the course ensures practical applicability. TR-18 and TR-19 focus on graphing sine, cosine, tangent, and cotangent functions, while TR-20 addresses secant and cosecant graphs. The domains and ranges of trigonometric functions are covered in TR-21, completing this suite of practical tools.

Inverse functions find their place with an algebra review in TR-22 and further exploration in TR-23 and TR-24, including detailed techniques for using calculators (TR-25). The problem-solving skills are honed with sections on solving right triangles (TR-26) and other triangle types (TR-27). Essential laws such as the Law of Sines (TR-28) and the Law of Cosines (TR-29) are thoroughly explained and proved (TR-29Z).

The SSA triangles overview in TR-30 and solving SSA triangles in TR-31 cap off the triangle-solving skills. The course then delves into trigonometric identities and proofs, starting with an introduction in TR-32 and elaborating on Pythagorean trig identities in TR-33, including their applications on the unit circle (TR-33Z). Techniques for using these identities (TR-34) and conjugate identities (TR-35), along with even and odd trig functions (TR-36) and reflections (TR-37), solidify this knowledge.

The complex sum and difference identities are demystified in TR-38 and TR-39, followed by double angle identities (TR-40) and half-angle identities (TR-41). The final segments of the course, including variations in trigonometric graphs (TR-42, TR-43, TR-44) and applications in polar coordinates (TR-45) and polar equations (TR-46), round off this extensive trigonometry series.

This methodically structured course ensures a deep understanding of trigonometry, from the very basics to intricate applications, making it an indispensable resource for students and educators alike.