Trigonometry: Free Course

About this course

Trigonometry connects angles, ratios and periodic functions. This course develops right-triangle reasoning, the unit circle, identities, inverse functions and models of repeating change. Study the complete public source playlist from Khan Academy in English, with all 71 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Connect triangle ratios with the unit circle.
• Work in degrees and radians.
• Analyze trigonometric graphs, identities and inverse functions.
• Solve triangles and model periodic behavior.

Skills you’ll gain

• Unit circle
• Trigonometric identities
• Periodic models
• Inverse trigonometry

Course Overview

Radian measure extends angle representation beyond degrees, and the unit circle connects sine and cosine with coordinates and symmetry. Graph examples examine amplitude, period, midline and transformations, while tangent and inverse-function lessons require careful attention to domain and range. Pythagorean and angle-addition identities support algebraic reasoning. The laws of sines and cosines extend triangle solving beyond right triangles. Applications include daily or seasonal variation and geometric measurement, with challenge problems retained alongside introductory material. Choose the angle unit deliberately, and remember that an inverse trigonometric function uses a restricted range rather than returning every angle with the same ratio.

How to study the course

• Videos 1–17: this part of the source list includes “Proof of angle addition formula for cosine” through “Introduction to radians”. State the quantities and conditions before calculating. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 18–35: this part of the source list includes “Tangent graph” through “Example: Amplitude and period”. Keep equivalent expressions or representations connected. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 36–53: this part of the source list includes “Example: Graph of cosine” through “Example: Trig to solve the sides and angles of a right triangle”. Check each operation with a small example before extending it. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 54–71: this part of the source list includes “Modeling annual temperature variation with trigonometry” through “Radian and degree conversion practice”. Explain a result in words as well as symbols. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, returning learners and anyone strengthening the specific mathematics named in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort with the preceding arithmetic or algebra skills is useful. Keep paper, a pencil and a calculator when a lesson uses one. Grade-specific courses assume the learner’s earlier grade-level knowledge.

Put the lessons into practice

Build a periodic model with a stated midline, amplitude and period, and explain each parameter in a fictional context. Solve a triangle using a suitable law, checking whether the available information determines the desired angle or side. Verify one identity algebraically and distinguish that task from solving a trigonometric equation for particular inputs.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.