Free online courseTrigonometry Course
Duration of the online course: 6 hours and 14 minutes
New course
Enroll in this comprehensive free online Trigonometry course covering angles, geometric proofs, the Pythagorean theorem, trig functions, identities, and graph variations.
Course Description
The "Trigonometry Course" is an immersive learning experience that spans over a comprehensive 6 hours and 14 minutes. This course, categorized under Basic Studies and more specifically under Trigonometry, provides a detailed and structured exploration of trigonometric principles, making it an essential resource for foundational mathematics education.
The course kicks off with TR-00, providing an engaging "Introduction to the Trigonometry Series." This sets the stage for the subsequent deep dive into the world of angles, beginning with TR-01, which introduces the basic concepts of angles, followed by TR-02 that elaborates on the different types of angles. TR-03 extends this knowledge to explore angle relationships, laying a solid groundwork for the measurements covered in TR-04 and the more advanced nuances of degrees, minutes, and seconds in TR-04Z.
Continuing the journey, the course transitions to radians in TR-05, which introduces the concept of radians, and TR-06 which delves into measuring angles in radians. This is complemented by a review of essential geometric concepts related to triangles in TR-07, including the first proof of Thales' Theorem in TR-07Z. The significance of triangles is further emphasized in TR-08, discussing similar and congruent triangles, followed by an exploration of the Pythagorean Theorem in TR-09 and its proof in TR-09Z. TR-10 introduces Pythagorean triples, enhancing the relationships between different types of triangles.
The course meticulously covers the distances between points, both in a plane (TR-11) and in space (TR-12), before introducing the core trigonometric ratios in TR-13, and the origins of co-trigonometric functions in TR-13Z. The unit circle, a fundamental concept in trigonometry, is covered in TR-14, followed by practical applications of sine and cosine values in common angles (TR-15) and their proofs (TR-15Z).
From using a calculator for trigonometric functions in TR-16 to exploring the most common uses of trigonometry in TR-17, the course ensures practical applicability. TR-18 and TR-19 focus on graphing sine, cosine, tangent, and cotangent functions, while TR-20 addresses secant and cosecant graphs. The domains and ranges of trigonometric functions are covered in TR-21, completing this suite of practical tools.
Inverse functions find their place with an algebra review in TR-22 and further exploration in TR-23 and TR-24, including detailed techniques for using calculators (TR-25). The problem-solving skills are honed with sections on solving right triangles (TR-26) and other triangle types (TR-27). Essential laws such as the Law of Sines (TR-28) and the Law of Cosines (TR-29) are thoroughly explained and proved (TR-29Z).
The SSA triangles overview in TR-30 and solving SSA triangles in TR-31 cap off the triangle-solving skills. The course then delves into trigonometric identities and proofs, starting with an introduction in TR-32 and elaborating on Pythagorean trig identities in TR-33, including their applications on the unit circle (TR-33Z). Techniques for using these identities (TR-34) and conjugate identities (TR-35), along with even and odd trig functions (TR-36) and reflections (TR-37), solidify this knowledge.
The complex sum and difference identities are demystified in TR-38 and TR-39, followed by double angle identities (TR-40) and half-angle identities (TR-41). The final segments of the course, including variations in trigonometric graphs (TR-42, TR-43, TR-44) and applications in polar coordinates (TR-45) and polar equations (TR-46), round off this extensive trigonometry series.
This methodically structured course ensures a deep understanding of trigonometry, from the very basics to intricate applications, making it an indispensable resource for students and educators alike.
Conteúdo do Curso
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Video class: TR-00: Introduction to Trigonometry Series by Dennis F. Davis
0h05m
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Exercise: What is the primary focus of the trigonometry series described?
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Video class: TR-01: Introduction to Angles (Trigonometry series by Dennis F. Davis)
0h06m
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Exercise: What is the standard position of an angle on the Cartesian coordinate system?
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Video class: TR-02: Types of Angles (Trigonometry series by Dennis F. Davis)
0h05m
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Exercise: What is a quadrantal angle?
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Video class: TR-03: Angle Relationships (Trigonometry series by Dennis F. Davis)
0h03m
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Exercise: When two angles share a vertex and one side but do not overlap, what is this pair of angles called?
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Video class: TR-04: Angle Measurement in Degrees (Trigonometry series by Dennis F. Davis)
0h05m
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Exercise: In trigonometry, which angle is often referred to as a common angle and represents a quarter of a full circle?
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Video class: TR-04Z: Degrees Minutes and Seconds (Trigonometry series by Dennis F. Davis)
0h06m
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Exercise: What is the decimal equivalent of an angle measured as 37 degrees, 25 minutes, and 50 seconds?
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Video class: TR-05: Introduction to Radians (Trigonometry series by Dennis F. Davis)
0h05m
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Exercise: What is the angle in radians subtended by an arc of length 5 meters on a circle with a radius of 5 meters?
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Video class: TR-06: Angle Measurement in Radians (Trigonometry series by Dennis F. Davis)
0h07m
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Exercise: Which of the following is equivalent to 120 degrees when expressed in radians?
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Video class: TR-07: Geometry Review of Triangles (Trigonometry series by Dennis F. Davis)
0h07m
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Exercise: In a triangle, if the vertex angle is 50 degrees, what are the measures of the base angles in an isosceles triangle?
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Video class: TR-07Z: First Proof Thales' Theorem (Trigonometry series by Dennis F. Davis)
0h02m
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Exercise: Given a circle with a diameter AB, if a point C is placed on the circumference of the circle, what type of angle does triangle ABC form at point C?
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Video class: TR-08: Similar and Congruent Triangles (Trigonometry series by Dennis F. Davis)
0h04m
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Video class: TR-09: The Pythagorean Theorem (Trigonometry series by Dennis F. Davis)
0h03m
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Exercise: In a right triangle, if the lengths of the two shorter sides are 5 meters and 12 meters, what is the length of the hypotenuse?
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Video class: TR-09Z: Proof of Pythagorean Theorem (Trigonometry series by Dennis F. Davis)
0h02m
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Exercise: In a right triangle, which of the following equations represents the Pythagorean theorem?
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Video class: TR 10: Pythagorean Triples (Trigonometry series by Dennis F. Davis)
0h03m
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Exercise: Which of the following sets of numbers is a Pythagorean triple?
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Video class: TR-11: Distance Between Points in a Plane (Trigonometry series by Dennis F. Davis)
0h03m
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Exercise: What is the distance between the points (3, 4) and (7, -2) on a Cartesian coordinate plane?
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Video class: TR-12: Distance Between Points in Space (Trigonometry series by Dennis F. Davis)
0h03m
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Exercise: If a point in 3D space has coordinates (3, 4, 5), what is the distance from the origin to this point?
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Video class: TR-13: The Trigonometric Ratios (Trigonometry series by Dennis F. Davis)
0h06m
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Exercise: Using the mnemonic SOHCAHTOA for trigonometric ratios, what is the cosine of an angle in a right triangle with an adjacent side of 6 units and a hypotenuse of 10 units?
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Video class: TR-13Z: How the Co- Trig Functions got their Names
0h03m
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Exercise: In a right triangle, if angle theta is the complement of angle beta, which of the following expressions is true regarding their trigonometric functions?
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Video class: TR-14: The Unit Circle (Trigonometry series by Dennis F. Davis)
0h06m
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Exercise: What is the value of the tangent function for an angle θ on the unit circle where the sine of θ is 0.6 and the cosine of θ is 0.8?
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Video class: TR-15: Sine and Cosine of Common Angles (Trigonometry series by Dennis F. Davis)
0h06m
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Exercise: Which of the following values is the sine of 135 degrees?
This free course includes:
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