Trigonometry Full Course
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In this full course, we will cover all the major topics of Trigonometry. Trigonometry is typically part of a Pre-Calculus course. Here, we will learn about the six Trigonometric functions (sine, cosine, cosecant, secant, tangent, and cotangent). We will then move on to study the unit circle, how to graph trigonometric functions, how to work with trigonometric identities, how to solve trigonometric equations, how to solve right triangles and oblique triangles (law of sines and cosines), how to work with vectors, and then finish up by discussing complex numbers in Trigonometry.
00:00:00 Angles
00:12:09 Degrees, Minutes, Seconds
00:24:53 Coterminal Angles
00:34:27 Similar Triangles
00:52:23 Trigonometric Functions
01:05:28 Reciprocal Identities
01:24:37 Pythagorean Identities
01:46:29 Trigonometric Functions of Acute Angles
02:05:59 Trigonometric Functions of Non-Acute Angles
02:26:36 Estimating Trigonometric Function Values
02:39:09 Solving Right Triangles
02:51:34 Radian Measure
03:03:26 Arc Length on a Circle
03:16:44 Unit Circle and Circular Functions
03:33:25 Linear and Angular Speed
03:47:18 Graphing Sine and Cosine
04:54:46 Graphing Tangent and Cotangent
06:14:48 Graphing Secant and Cosecant
07:17:32 Fundamental Identities
07:37:03 Verifying Trigonometric Identities
07:59:41 Sum and Difference Identities for Cosine
08:31:24 Sum and Difference Identities for Sine and Tangent
08:57:31 Double-Angle, Product-to-Sum, and Sum-to-Product Identities
09:23:29 Half-Angle Identities
09:43:23 Inverse Trigonometric Functions
11:01:40 Solving Trigonometric Equations Part 1 (Linear)
11:18:08 Solving Trigonometric Equations Part 2 (Factoring)
11:44:17 Solving Trigonometric Equations Part 3 (Identities)
12:04:29 Solving Trigonometric Equations Part 4 (Half-Angles)
12:25:47 Solving Trigonometric Equations Part 5 (Multiple Angles)
13:01:08 Solving Trigonometric Equations Part 6 (Inverse Trig Functions)
14:04:00 Solving Trigonometric Inequalities
14:34:10 Law of Sines (Oblique Triangles) and Area of a Triangle
14:56:19 Law of Sines (Ambiguous Case)
15:30:37 Law of Cosines and Heron's Formula
16:06:13 Introduction to Vectors (Magnitude and Direction Angle)
16:30:29 Operations with Vectors
16:46:18 Dot Product and Angle Between Vectors
17:13:58 Review of Complex Numbers
17:39:18 Polar Form of a Complex Number
18:08:42 The Product and Quotient Theorem
18:47:15 De Moivre's Theorem
19:32:58 Polar Coordinates
20:05:56 Distance Between Polar Points
20:32:05 Lines in Polar Form
21:02:12 Circles in Polar Form
21:58:35 Inclination of a Line
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