28.98 GB | 38min 18s | mp4 | 1280X720 | 16:9
Genre:eLearning |Language:English
Files Included :
1 Introduction to the course.mp4 (75.45 MB)
2 What is trigonometry.mp4 (7.16 MB)
3 Place of trigonometry in mathematics and sciences.mp4 (27.69 MB)
4 Warning inverse versus reciprocal.mp4 (60.52 MB)
5 One, three, six, nine, twelve functions.mp4 (44.63 MB)
6 Various ways of defining the sine function; trigonometric vs circular.mp4 (52.22 MB)
7 What you are going to learn and why.mp4 (47.88 MB)
8 Proportions and their crucial role in this course.mp4 (65.84 MB)
1 How to use this section.mp4 (49.42 MB)
10 Area of a triangle; the height (altitude).mp4 (41.13 MB)
11 Isometries line and point symmetries, rotations, translations.mp4 (87.69 MB)
12 Thales' theorem and similar triangles.mp4 (125.02 MB)
13 Right triangles and Pythagorean theorems.mp4 (82.58 MB)
14 Important facts about equilateral and isosceles triangles.mp4 (202.92 MB)
15 Back to Euclidean distance how to compute it in the coordinate system.mp4 (50.82 MB)
16 Circles a geometrical definition and equation in the coordinate system.mp4 (46.45 MB)
17 Inscribed and central angles.mp4 (198.95 MB)
18 Circumscribed and inscribed circles for triangles; bisectors.mp4 (83.68 MB)
19 When is it possible to circum-in-scribe a circle aroundin a quadrilateral.mp4 (88.74 MB)
2 Euclidean geometry Primitive notions, axioms, definitions, and theorems.mp4 (101.2 MB)
20 The sum of angles in a polygon; the interior angle in a regular polygon.mp4 (270.25 MB)
3 Angles definition, usual notation, measures, kinds of angles.mp4 (74.76 MB)
4 Angle-related terminology.mp4 (30.44 MB)
5 Triangles definition and usual notation; congruent triangles SSS, SAS, ASA.mp4 (85.37 MB)
6 Optional Euclidean distance and triangle inequality.mp4 (66.47 MB)
7 Fifth postulate and alternate angles; parallelograms.mp4 (132.7 MB)
8 The sum of angles in a triangle, and some consequences.mp4 (37.56 MB)
9 The concept of area; area of a rectangle.mp4 (124.61 MB)
1 Length and area not always easy.mp4 (26.86 MB)
2 A very early approximation.mp4 (36.62 MB)
3 Archimedes and approximations by perimeters of regular polygons.mp4 (324.82 MB)
4 What about the area of a disk An intuitive answer.mp4 (37.67 MB)
5 What about the area of a disk A hardcore answer (Eudoxus).mp4 (63.7 MB)
1 Where to find geometry for this section.mp4 (55.06 MB)
10 Some remarks about the tangent function.mp4 (56.93 MB)
2 Six possible ratios and why they describe functions; Cofunction Identities.mp4 (114.94 MB)
3 Six trigonometric functions, Exercise 1.mp4 (436.41 MB)
4 Six trigonometric functions, Exercise 2.mp4 (204.29 MB)
5 Some special triangles, Exercise 3.mp4 (168.97 MB)
6 One half of a square the 45-45-90 triangles, Exercise 4.mp4 (224.13 MB)
7 The Pythagorean Identities, Exercise 5.mp4 (390.92 MB)
8 Starting plotting the sine function.mp4 (87.21 MB)
9 It is enough to plot the sine in order to get the cosine.mp4 (49.23 MB)
1 Stage 0 what we already know about the sine curve (0, 45, 90).mp4 (9.05 MB)
10 Sine and cosine of triple angles, Problem 6.mp4 (185.85 MB)
11 Computing sine of 18 degrees using the formulas for double and triple angles.mp4 (371.2 MB)
12 Tangent of 22 5 degrees by elegant geometry, Problem 8.mp4 (14.93 MB)
13 Sine and cosine of 22 5 degrees by half angle formulas, Problem 9.mp4 (140.23 MB)
14 A cool trick for computing sine and cosine of half of an angle, Problem 10.mp4 (265.62 MB)
15 Same trick one more time, Problem 11.mp4 (138.35 MB)
16 Different looks of sine and cosine of 15 degrees, Problem 12.mp4 (142.83 MB)
17 An identity to prove, Problem 13.mp4 (90.62 MB)
18 Tangent half-angle formulas, Problem 14.mp4 (462.53 MB)
19 Experimenting with double angle formulas, Problem 15.mp4 (169.79 MB)
2 Equilateral triangle and the 30-60-90 triangles, Problem 1.mp4 (164.99 MB)
20 Summary Section 5.mp4 (25.48 MB)
3 Derivation of the sum identity for sine, using geometry; Method 1.mp4 (81.69 MB)
4 Derivation of the sum identities for sine and cosine, using method 2.mp4 (194.34 MB)
5 Conclusion Double Angle Formulas and Power Reduction Formulas.mp4 (207.45 MB)
6 Half Angle Formulas, Problem 2.mp4 (268.55 MB)
7 Applications of the sum identities, Problem 3.mp4 (117.98 MB)
8 A geometric way of computing sine and cosine of 18 and 72 degrees, Problem 4.mp4 (246.79 MB)
9 A geometric way of computing sine and cosine of 54 and 36 degrees, Problem 5.mp4 (263.61 MB)
1 Inverse trigonometric functions arcsine, arccosine, arctangent.mp4 (69.7 MB)
2 What does it mean to solve a triangle.mp4 (27.37 MB)
3 Solving right triangles, with or without approximations.mp4 (571.9 MB)
4 More (elementary) problem solving.mp4 (239.9 MB)
5 A difficult problem.mp4 (280.97 MB)
1 Why we need a new way of measuring angles.mp4 (33.53 MB)
2 What is radian and how to work with it.mp4 (56.66 MB)
3 The angles in radians to remember, and how to do it.mp4 (69.81 MB)
4 Degree to radian (and back) conversion, exercises.mp4 (10.43 MB)
5 Angles in the coordinate system some terminology (continuation after V11).mp4 (69.9 MB)
1 What we have by now.mp4 (59.97 MB)
2 What we want to have.mp4 (29.7 MB)
3 Wrapping the number axis (the t-axis) around the unit circle.mp4 (63.42 MB)
4 Definition of circular functions sine and cosine, approach 1.mp4 (91.78 MB)
5 Definition of circular functions sine and cosine, approach 2.mp4 (52.79 MB)
1 From sine and cosine as functions of one real variable to 6 circular functions.mp4 (96.02 MB)
10 The cotangent function, its properties and graph.mp4 (57.96 MB)
11 The cosecant function, its properties and graph.mp4 (28.23 MB)
12 The secant function, its properties and graph.mp4 (27.33 MB)
13 The names of the circular functions.mp4 (57 MB)
14 Circular functions, Exercise 4.mp4 (192.11 MB)
15 Circular functions, Exercise 5.mp4 (228.5 MB)
2 The signs of the circular functions in different quadrants, Exercise 1.mp4 (158.2 MB)
3 Reference angles and their wonderful applicability.mp4 (115.38 MB)
4 Exact values of sine and cosine of various angles, Exercise 2.mp4 (219.22 MB)
5 Pythagorean triples Finding values of cofunctions, Exercise 3.mp4 (147.35 MB)
6 Periodic functions.mp4 (57.21 MB)
7 The sine function, its properties and graph.mp4 (136.8 MB)
8 The cosine function, its properties and graph.mp4 (55.15 MB)
9 The tangent function, its properties and graph.mp4 (52.47 MB)
1 So much will be recycled!.mp4 (64.03 MB)
10 How to scale any pair of real numbers into the sine and cosine of some angle.mp4 (39.01 MB)
11 A linear combination of the sine and the cosine.mp4 (114.6 MB)
12 A linear combination of the sine and the cosine, Exercise 1.mp4 (295.4 MB)
13 Find max and min, Exercise 2.mp4 (163.18 MB)
14 Even Odd Identities, Exercise 3.mp4 (25.08 MB)
15 Sum and Difference Identities, Exercise 4.mp4 (257.33 MB)
16 Sum and Difference Identities, Exercise 5.mp4 (321.71 MB)
17 Applications of Double Angle Formulas, Exercise 6.mp4 (260.42 MB)
18 Applications of Double Angle Formulas, Exercise 7.mp4 (175.06 MB)
19 Product To Sum Formulas.mp4 (133.68 MB)
2 Derivation of the sum identity for the cosine in a general case.mp4 (145.05 MB)
20 Product To Sum Formulas, Exercise 8.mp4 (33.69 MB)
21 Sum To Product Formulas.mp4 (164.81 MB)
22 Sum To Product Formulas, Exercise 9.mp4 (249.42 MB)
23 Monotonicity of the sine in the first quadrant.mp4 (254.92 MB)
24 Monotonicity of the cosine in the first quadrant.mp4 (92.35 MB)
25 A preparation for arcsine, Exercise 10.mp4 (255.31 MB)
26 A preparation for arctangent, Exercise 11.mp4 (249.57 MB)
3 Derivation of the sum identity for the sine in a general case.mp4 (92.83 MB)
4 Derivation of the difference identity for the cosine in a general case.mp4 (61.63 MB)
5 Derivation of the difference identity for the sine in a general case.mp4 (188.55 MB)
6 Graph transformations, an introduction.mp4 (52.21 MB)
7 Sinusoids some terminology.mp4 (51.58 MB)
8 Some basic transformations of the sinusoid.mp4 (90.75 MB)
9 Non-sinusoidal circular functions to study from the book.mp4 (55.9 MB)
1 How to get around the no-injection issue.mp4 (68.34 MB)
10 Inverse trigonometric functions, Exercise 4.mp4 (360.96 MB)
2 Arcsine its properties and graph.mp4 (99.3 MB)
3 Arccosine its properties and graph.mp4 (72.68 MB)
4 Arctangent its properties and graph.mp4 (74.27 MB)
5 Why such names.mp4 (26.64 MB)
6 The link between inverse trigonometric functions and trigonometric equations.mp4 (120.5 MB)
7 Inverse trigonometric functions, Exercise 1.mp4 (150.5 MB)
8 Inverse trigonometric functions, Exercise 2.mp4 (253.81 MB)
9 Inverse trigonometric functions, Exercise 3.mp4 (273.19 MB)
1 Identities we have seen until now.mp4 (37.3 MB)
10 Identities, Exercise 8.mp4 (230.25 MB)
2 How to prove identities.mp4 (37.24 MB)
3 Identities, Exercise 1.mp4 (219.6 MB)
4 Identities, Exercise 2.mp4 (284.05 MB)
5 Identities, Exercise 3.mp4 (142.34 MB)
6 Identities, Exercise 4.mp4 (175.73 MB)
7 Identities, Exercise 5.mp4 (311.96 MB)
8 Identities, Exercise 6.mp4 (159.2 MB)
9 Identities, Exercise 7.mp4 (362.93 MB)
1 What is a trigonometric equation or inequality.mp4 (49.6 MB)
10 Reducing the degree of trigonometric functions, Problem 6.mp4 (91.36 MB)
11 Universal Substitution tangent of half argument, Problem 7.mp4 (444.83 MB)
12 Homogenous equations, Problem 8.mp4 (187.28 MB)
13 Combinations of the methods above, Problem 9.mp4 (408.23 MB)
14 A difficult one, Problem 10.mp4 (52.82 MB)
15 Another difficult one, Problem 11.mp4 (80.35 MB)
2 What is the difference between a trigonometric equation and identity.mp4 (24.11 MB)
3 Functional equations and inequalities and their graphical illustrations.mp4 (51.78 MB)
4 Inequalities and equations you can solve without any computations.mp4 (60.16 MB)
5 The very basic types of trigonometric equations, Problem 1.mp4 (259 MB)
6 Using sum or difference identities for sine and cosine, Problem 2.mp4 (205.62 MB)
7 Factorization Sum-To-Product Formulas, Problem 3.mp4 (267.92 MB)
8 Factorization of polynomials, Problem 4.mp4 (141.07 MB)
9 Using the Product-To-Sum Formulas, Problem 5.mp4 (293.42 MB)
1 Tangent and slopes of straight lines in the 2D coordinate system.mp4 (86.59 MB)
10 Rotations and their matrices.mp4 (58.64 MB)
11 Complex numbers rectangular and polar form.mp4 (124.01 MB)
12 Multiplication of complex numbers and the Sum Identities for the sine and cosine.mp4 (243.89 MB)
13 De Moivre's formulas for taking powers of complex numbers.mp4 (309.11 MB)
14 Roots of unity.mp4 (61.75 MB)
15 Harmonic motion reading recommendations.mp4 (22.23 MB)
2 How to compute the angle between two lines in the 2D coordinate system.mp4 (51.54 MB)
3 The Law of Cosines as a generalization of Pythagorean Theorem.mp4 (78.91 MB)
4 A sine-based formula for the area of a triangle.mp4 (19.11 MB)
5 The Law of Sines.mp4 (44.25 MB)
6 Heron's Formula.mp4 (27.43 MB)
7 Solving oblique triangles.mp4 (31.08 MB)
8 Vectors in the plane (or in the 3-space) and angles between them.mp4 (68.61 MB)
9 The dot product and projection; cross product and scalar triple product.mp4 (54.06 MB)
1 The limit of (sin x)x in zero, and its importance in Calculus.mp4 (111.76 MB)
10 Parametric curves.mp4 (83.45 MB)
11 Power Reduction Formulas and integration.mp4 (31.36 MB)
12 Trigonometric substitutions in integrals.mp4 (33.52 MB)
2 The slope of a straight line and its importance for Differential Calculus.mp4 (99.33 MB)
3 Differentiability of the sine and cosine which formulas to use.mp4 (225.96 MB)
4 The derivatives of sine, cosine, tangent, arcsine and arctangent; some visuals.mp4 (97 MB)
5 Interesting examples of sine-based functions.mp4 (100.49 MB)
6 A word about Fourier, spirographs, Euler's formula, and Euler's identity.mp4 (60.35 MB)
7 Trigonometric functions in solutions of differential equations.mp4 (26.92 MB)
8 Polar coordinates in the plane.mp4 (51.86 MB)
9 Cylindrical and spherical coordinates in the 3-space.mp4 (61.34 MB)
1 How to use this section.mp4 (36.63 MB)
10 Problem 9.mp4 (115.79 MB)
11 Problem 10.mp4 (161.43 MB)
12 Problem 11.mp4 (405.5 MB)
13 Problem 12.mp4 (53.64 MB)
14 Problem 13.mp4 (141.12 MB)
15 Problem 14.mp4 (334.25 MB)
16 Problem 15.mp4 (198.4 MB)
17 Problem 16.mp4 (268.97 MB)
18 Problem 17.mp4 (169.05 MB)
19 Problem 18.mp4 (497.22 MB)
2 Problem 1.mp4 (184.44 MB)
20 Problem 19.mp4 (209.36 MB)
21 Problem 20.mp4 (296.84 MB)
22 Problem 21.mp4 (87.84 MB)
23 Problem 22.mp4 (151.03 MB)
24 Problem 23.mp4 (83.65 MB)
25 Problem 24 one of the nicest problems ever, with two really cool solutions.mp4 (174.25 MB)
26 Problem 25 my favourite problem with many ways of solving it.mp4 (178.91 MB)
27 Precalculus 3, Wrap-up.mp4 (2.47 MB)
3 Problem 2.mp4 (319.14 MB)
4 Problem 3.mp4 (43.2 MB)
5 Problem 4.mp4 (198.17 MB)
6 Problem 5.mp4 (110.52 MB)
7 Problem 6.mp4 (202.59 MB)
8 Problem 7.mp4 (294.85 MB)
9 Problem 8.mp4 (419.23 MB)
1 Bonus Lecture.mp4 (33.54 MB)]
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