Free online courseTrigonometry

Course Description

Trigonometry is an in-depth course designed to cover all foundational aspects of trigonometry. With a duration of 16 hours and 32 minutes, this course is ideal for those embarking on their journey in the world of trigonometry, especially within the realm of basic studies. Although it is yet to receive reviews, the meticulously structured curriculum promises to equip learners with comprehensive knowledge in trigonometric principles and applications.

The course begins by introducing the concept of standard position angles. Students will learn the fundamental properties and definitions that form the backbone of trigonometry. The subsequent section further deepens this understanding, exploring more complex properties and their applications.

Transitioning into angle measurement, students will cover the conversion between degrees and radians, a vital skill for any trigonometry enthusiast. They'll then delve into more detailed measures, learning how to express angles in degrees and minutes, ensuring a solid comprehension of angular units.

Setting up the Unit Circle is a critical skill in trigonometry, and this course dedicates significant time to it. This topic is split into two parts, starting with the essential framework and moving onto reference angles, thereby providing a clear graphical representation of trigonometric functions.

The concept of linear motion is also examined, providing students with the ability to evaluate trigonometric functions using the unit circle, specifically in degrees. Fundamental trigonometric identities are introduced, with a focus on understanding and simplifying trig expressions.

Applications of right triangle trigonometry encompass finding missing sides and solving for acute angles, enhancing problem-solving skills essential for practical applications. The course also covers trigonometric cofunctions and extends to evaluate the trigonometric functions of any angle, fostering a deeper conceptual understanding.

Key trigonometric functions like sine and cosine are explored thoroughly, including their graphing and equations derived from graphical data. Practical problems such as modeling water depth with sinusoidal functions provide a real-world context and application.

Further topics include tangent and secant functions, graphing techniques, and evaluating inverse trigonometric functions, broadening the analytical toolkit of the learner. The verification of trigonometric identities, an integral part of advanced trigonometry, is tackled through multiple instructional segments, ensuring thorough comprehension.

The course also touches on advanced trigonometric identities, including sum and difference formulas and half and double angles, followed by rigorous trigonometric proofs, enhancing logical reasoning and proof skills.

Solving trigonometric equations is another crucial aspect, encompassing single and multiple angle scenarios, both within restricted ranges and all solutions, providing a complete understanding of trigonometric dynamics.

Oblique triangles are addressed through the law of sines and cosines, including the ambiguous case, and applications of these laws are discussed. The calculation of the area using Heron's formula is also covered, rounding out the learner’s ability to tackle complex problems.

Additionally, the course delves into the fascinating realm of polar coordinates and transformations between polar and rectangular systems. Graphing polar equations and examining symmetry further expand the learner’s perspective, followed by an introduction to complex numbers in polar form and De Moivre's Theorem.

Finally, the course concludes with an introduction to vectors, including their properties, applications, dot products, and vector projections, culminating in practical examples such as trigonometry bearing problems and navigation. This end-to-end journey ensures a robust and comprehensive under