Mastering Trigonometric Ratios and SOH CAH TOA

The Organic Chemistry Tutor

This comprehensive mathematics tutorial introduces the fundamental concepts of trigonometric ratios within right-angled triangles. The video systematically explains the definitions of sine, cosine, and tangent using the mnemonic device SOH CAH TOA, demonstrating how to identify the opposite, adjacent, and hypotenuse sides relative to a specific angle. Through clear, hand-drawn examples on a blackboard style interface, the narrator guides viewers from basic ratio identification to more complex applications involving special right triangles and inverse functions. The content covers several key topics including calculating ratios for standard triangles (like 8-15-17 and 3-4-5), determining exact trigonometric values for special angles (30, 45, and 60 degrees), and summarizing these values in a reference table. The video progresses to practical problem-solving techniques, showing students how to use algebra to find missing side lengths when given an angle and one side, as well as how to use inverse trigonometric functions (specifically arctan) to calculate missing angles when given two sides. Ideally suited for high school geometry and trigonometry classes, this video serves as both an introduction and a practice resource. The narrator frequently encourages active learning by prompting viewers to pause the video and attempt problems before seeing the solution. This format allows teachers to use the video as an interactive classroom tool for direct instruction, guided practice, or independent review, effectively addressing common student difficulties in setting up and solving trigonometric equations.