Free Course Image Trigonometry

Free online courseTrigonometry

Duration of the online course: 6 hours and 35 minutes

4.62

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(39)

Learn trigonometry with Khan Academy's free online course. Master topics like trig functions, identities, unit circle, graphing, and word problems. Perfect for beginners!

In this free course, learn about

  • Foundations of Right Triangle Trigonometry
  • Right Triangle Applications of Trig Functions
  • Unit Circle and Basic Trig Graphs
  • Graphing and Identifying Trigonometric Functions
  • Core Trigonometric Identities and Angle Addition
  • Advanced Trig Identities and Symmetry
  • Applied Trigonometry and Law of Cosines
  • Law of Sines and Modeling Motion
  • Unit Circle Review and Introduction to Polar Coordinates
  • Polar to Cartesian and Inverse Trig Functions
  • Inverse Cosine and Double-Angle Identities
  • IIT JEE Trigonometry: Expressions and Optimization
  • Trig Systems and Challenge Geometry Problems

Course Description

Trigonometry is an engaging and comprehensive course designed for learners who aim to grasp the fundamental concepts and applications of trigonometry. With a total duration of 6 hours and 35 minutes, this course efficiently covers various topics essential for understanding trigonometric functions, identities, and their real-world applications.

Rated 5 out of 5 stars, the course has garnered positive feedback from students who appreciate its structured approach and clarity. This high rating signifies the course's effectiveness and the value it delivers to learners, making it a trusted resource for anyone looking to strengthen their trigonometry skills.

Belonging to the Basic Studies category, under the Trigonometry subcategory, the course methodically breaks down complex concepts into digestible lessons, allowing students to build a solid foundation in trigonometry. The coursework begins with an introduction to basic trigonometric functions and progresses to more advanced topics such as the unit circle, graphing trigonometric functions, and trigonometric identities.

Throughout the course, learners will delve into detailed discussions on the radian and degree measures, unit circle definitions, and the applications of trigonometric functions. These foundational topics are crucial for mastering the subject and understanding its applications in various fields of study and professional practices.

Advanced sections of the course cover graphing trig functions, analyzing their graphs, and solving more complex trigonometric equations. These lessons are designed to help students visualize and interpret trigonometric functions accurately, enhancing their problem-solving skills and analytical abilities.

Students also explore various trigonometric identities and their proofs, gaining insights into mathematical reasoning and logic. The course offers clear explanations and demonstrations of proofs such as sin(a+b), cos(a+b), and other fundamental identities, ensuring learners can apply these concepts confidently in different mathematical contexts.

Utilizing real-world problems and scenarios, the course includes trigonometry word problems, navigation problems, and engaging applications like Ferris wheel and polar coordinates problems. These practical examples help solidify theoretical knowledge by demonstrating how trigonometry can solve real-life challenges.

Additionally, the course covers inverse trigonometric functions, parametric equations, and polar coordinates, broadening the learners' understanding and preparing them for more advanced mathematical studies. The inclusion of fun and challenging problems, such as the area of triangles and hexagons, further enriches the learning experience, making trigonometry both enjoyable and intellectually stimulating.

Overall, Trigonometry is a well-rounded course that provides comprehensive coverage of trigonometric concepts, ensuring learners develop a deep and practical understanding of the subject. Its structured lessons, high rating, and engaging content make it an excellent choice for anyone looking to master trigonometry.

Course content

  • Video class: Basic trigonometry | Basic trigonometry | Trigonometry | Khan Academy 09m
  • Exercise: _What does the "trig" in trigonometry literally mean?
  • Video class: Basic trigonometry II | Basic trigonometry | Trigonometry | Khan Academy 12m
  • Exercise: What is the sine of 30 degrees in a 30-60-90 triangle?
  • Video class: Radian and degree | Unit circle definition of trig functions | Trigonometry | Khan Academy 09m
  • Exercise: _How many degrees are there in one radian according to the presentation?
  • Video class: Using Trig Functions 10m
  • Exercise: What is the length of the adjacent side of a right triangle given the hypotenuse and angle pi/4 radians?
  • Video class: Using Trig Functions Part II 08m
  • Exercise: _What trigonometric function should be used to solve for the green side in the given problem?
  • Video class: The unit circle definition of trigonometric function 09m
  • Exercise: How does the unit circle extend the definition of trigonometric functions?
  • Video class: Unit Circle Definition of Trig Functions 10m
  • Exercise: _What is the mnemonic used to memorize the definitions of sine, cosine, and tangent functions in a right triangle?
  • Video class: Graph of the sine function 07m
  • Exercise: What is the sine of pi radians on a unit circle?
  • Video class: Graphs of trig functions 10m
  • Exercise: _What is the period of the sine function?
  • Video class: Graphing trig functions 09m
  • Exercise: What is the period of the function f(x) = 2 sine of 1/2 x?
  • Video class: More trig graphs 05m
  • Exercise: _What is the amplitude of the function shown in the graph?
  • Video class: Determining the equation of a trigonometric function 09m
  • Exercise: Identify the Trigonometric Function Type
  • Video class: Trigonometric Identities 09m
  • Exercise: _What is the Pythagorean theorem?
  • Video class: Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b) 09m
  • Exercise: What is the sine of (alpha + beta) equal to?
  • Video class: Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b) 09m
  • Exercise: _What is the trigonometric identity being derived in this text?
  • Video class: Trig identities part 2 (part 4 if you watch the proofs) | Trigonometry | Khan Academy 09m
  • Exercise: What is the identity for cotangent in terms of secant and cosecant?
  • Video class: Trig identities part 3 (part 5 if you watch the proofs) | Trigonometry | Khan Academy 08m
  • Exercise: What is the result of applying the cosine function to a negative angle?
  • Video class: Trigonometry word problems (part 1) 09m
  • Exercise: How far does the ship need to travel to reach point B after traveling off course?
  • Video class: Trigonometry word problems (part 2) 02m
  • Exercise: _What is the value of m in the equation 125 - 100 cosine of 15 degrees?
  • Video class: Proof of the law of cosines | Trig identities and examples | Trigonometry | Khan Academy 09m
  • Exercise: What is the Law of Cosines?
  • Video class: Navigation Word Problem 08m
  • Exercise: What was the smuggling boat's average speed given the angles and speeds described?
  • Video class: Proof: Law of sines | Trig identities and examples | Trigonometry | Khan Academy 06m
  • Exercise: What does the Law of Sines relate in a triangle?
  • Video class: Ferris Wheel Trig Problem 07m
  • Exercise: _What is the radius of the ferris wheel in meters?
  • Video class: Ferris Wheel Trig Problem (part 2) 09m
  • Exercise: What is the function for the height of the Ferris wheel?
  • Video class: Fun Trig Problem 10m
  • Exercise: _What is the basic trig identity that comes out of the unit circle definition of trig functions?
  • Video class: Polar coordinates 1 | Parametric equations and polar coordinates | Precalculus | Khan Academy 10m
  • Exercise: What are the Cartesian coordinates of a point 3 steps right and 4 steps up?
  • Video class: Polar coordinates 2 | Parametric equations and polar coordinates | Precalculus | Khan Academy 09m
  • Exercise: _What is the equation for converting polar coordinates to Cartesian coordinates?
  • Video class: Polar coordinates 3 | Parametric equations and polar coordinates | Precalculus | Khan Academy 07m
  • Exercise: What is the Cartesian equation for polar function r = 4sin(θ)?
  • Video class: Inverse trig functions: arcsin | Trigonometry | Khan Academy 10m
  • Exercise: What is the arcsine of sqrt(2)/2?
  • Video class: Inverse trig functions: arctan | Trigonometry | Khan Academy 10m
  • Exercise: What is the value of the arctangent of -1?
  • Video class: Inverse trig functions: arccos | Trigonometry | Khan Academy 13m
  • Exercise: What is the value of arc cosine(-1/2) in degrees?
  • Video class: Trigonometry identity review/fun | Trig identities and examples | Trigonometry | Khan Academy 11m
  • Exercise: What is the correct trigonometric identity for cos(2a)?
  • Video class: Tau versus pi | Graphs of trig functions | Trigonometry | Khan Academy 16m
  • Exercise: What is the relationship between pi and tau in circle measurement?
  • Video class: IIT JEE trigonometry problem 1 | Trig identities and examples | Trigonometry | Khan Academy 15m
  • Exercise: If the angles A, B, and C of a triangle are in an arithmetic progression, what is the value of the expression a/c sin(2C) + c/a sin(2A)?
  • Video class: IIT JEE trigonometric maximum | Trig identities and examples | Trigonometry | Khan Academy 09m
  • Exercise: What is the maximum value of the expression 1/(sin²θ + 3sinθcosθ + 5cos²θ)?
  • Video class: IIT JEE trigonometric constraints | Trig identities and examples | Trigonometry | Khan Academy 12m
  • Exercise: How many values of θ satisfy the given conditions?
  • Video class: Trigonometric system example | Trig identities and examples | Trigonometry | Khan Academy 11m
  • Exercise: How many possible values of θ, between 0 and π, satisfy the given system of equations?
  • Video class: Trig challenge problem: area of a triangle | Khan Academy 16m
  • Exercise: Find the value of m + n + p in triangle CDM
  • Video class: Trig challenge problem: area of a hexagon | Math for fun and glory | Khan Academy 18m
  • Exercise: Calculate the sum of specific integers representing the hexagon's area.

This free course includes:

6 hours and 35 minutes of online video course

Digital certificate of course completion (Free)

Exercises to train your knowledge

100% free, from content to certificate

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