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Trigonometry - Comprehensive Course on Ratios, Laws, and Applications

Jeremy Klassen via YouTube

Overview

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Learn fundamental and advanced trigonometric concepts through comprehensive lessons covering primary trigonometric ratios, triangle classification, and the Pythagorean theorem. Master SOHCAHTOA principles for finding sides and angles in right triangles, then progress to more complex applications including the Sine Law and Cosine Law for solving non-right triangles. Explore transformations of sinusoidal functions, three-dimensional trigonometry problems, and real-world applications involving angles of elevation and depression. Practice solving multi-step problems such as finding heights of buildings and cliffs, calculating distances between objects, determining bridge spans, and working with guy wires and flagpoles. Develop skills in direction notation, sector area calculations, and solving problems involving overlapping triangles, parallelograms, and regular polygons. Apply trigonometric principles to practical scenarios including navigation problems with boats, projectile angles for sports, and architectural measurements, building proficiency through extensive problem-solving exercises and mixed practice sessions.

Syllabus

Math 30 1 Transformations of Sinusoidal Functions Lesson
Math 30 3 Triangle Area and the Pythagorean Theorem Lesson
Math 30 3 Classifying Triangles Lesson
Math 30 3 A Review of the Primary Trigonometric Ratios Lesson
Math 30 3 Multiple Triangle Problems Lesson
Math 30 3 Using the Sine Law to find Sides Lesson
Math 30 3 Using the Sine Law to Find an Angle Lesson
Math 30 3 Using the Cosine Law to Find Sides Lesson
Math 30 3 Using the Cosine Law to Find Angles Lesson
Math 30 3 Mixed Practice in Trigonometry Lesson
IB Applications of Direction Notation and Trigonometry Lesson
IB The Area of a Sector Lesson
Three Dimensional Trignometry Problem
Math 20 3 SOHCAHTOA Part I Lesson
Math 20 3 Finding the Sides of a Triangle Lesson
Math 20 3 Choosing a Ratio and Solving Lesson
Math 20 3 Multiple Triangle Problems Lesson
Math 20 3 Applications of Trigonometry Lesson
Math 20 3 Extra Practice with Trignometry Lesson
Math 30 1 Finding Trigonometric Functions given their Graphs Lesson
Finding x in two overlapping right triangles 1a
Finding x in two triangles sharing a side 1b
Finding the distance from a 47 m tall flagpole 2
Finding x with pythagoren thm and theta with arctan 3a
Finding x and y with the pythagorean theorem and trigonometry
Find the length of PQ using the tangent ratio twice 4
Finding the angle of elevation and length of a guy wire 5
Finding the height of a building and the angle of elevation 6
Finding the angle of depression and the height of a building 7
Finding the height and span of a bridge 8
Finding side b using the Sine Law 9
Finding side b using the Cosine Law 10
Solving for q by cross multiplying 11
Find angle A using the Cosine Law 12
Find side f using the Cosine Law 13
Find the distance between anchors and the height of a flagpole 14
Finding when I can use the Cosine Law 15
Finding the distance the anchors are away using Cosine Law 16
Finding the large angle in a parallelogram 17
Finding a missing angle using the sine law 18
Finding the distance between the anchors of two guy wires 19
Finding the height of an unaccessible cliff 20
Find how far apart the boats are after two hours 21
Find the angle within which a puck is shot 22
Find the height of a cliff using angles of elevation 23
Find the perimeter of a regular decagon 24
Finding the height of a kite 25

Taught by

Jeremy Klassen

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