--- title: Unit Circle description: The unit circle is a circle of radius one centered at the origin, used to define trigonometric functions for all real numbers. Learners will understand how to find exact values of sine, cosine, and tangent using radian and degree measurements. category: mathematics subcategory: geometry-and-trigonometry difficulty: beginner, intermediate, advanced url: /subject/unit-circle --- # Unit Circle The unit circle is a circle of radius one centered at the origin, used to define trigonometric functions for all real numbers. Learners will understand how to find exact values of sine, cosine, and tangent using radian and degree measurements. ## Available Resources 2 Courses • 4 Websites ## Websites ### 1. MathsIsFun Unit Circle A Math Is Fun page introducing the unit circle with an interactive diagram showing how sine, cosine and tangent correspond to lengths as the angle changes. Learners understand where the trigonometric ratios come from and how their signs vary by quadrant. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.mathsisfun.com/geometry/unit-circle.html **Tags:** unit-circle, trigonometry, sine-and-cosine, interactive ### 2. OpenStax Algebra and Trigonometry 2e — 7.3 Unit Circle Section 7.3 of OpenStax's peer-reviewed open textbook redefines sine and cosine via the unit circle. Covers special angles of 30, 45, and 60 degrees, domain and range, reference angles, and the Pythagorean identity, with worked examples. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://openstax.org/books/algebra-and-trigonometry-2e/pages/7-3-unit-circle **Tags:** unit-circle, trigonometry, sine-and-cosine, reference-angles, pythagorean-identity ### 3. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry ### 4. mathsisfun.com MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathsisfun.com **Tags:** websites, mathematics-statistics, algebra ## Courses ### 1. Trigonometry Khan Academy Master law of sines & cosines with Sal Khan's free Trigonometry course! Ace triangles & trigonometry calculations. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/trigonometry **Tags:** trigonometry, law-of-sines, law-of-cosines, unit-circle ### 2. Khan Academy: The Unit Circle Definition of Sine, Cosine, and Tangent **Author:** Sal Khan Free unit from Khan Academy's trigonometry course extending sine, cosine, and tangent from right triangles to the full unit circle. Includes video lessons, radian conversion, Pythagorean identity work, and graded practice exercises with instant feedback. It actually builds the unit-circle definition from right-triangle trig and tests retention with exercises. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func **Tags:** unit-circle, trigonometry, radians, trigonometric-functions, pythagorean-identity ## Youtubes ### 1. Trigonometry Fundamentals — Lockdown Live Math Ep. 2 **Author:** Grant Sanderson Grant Sanderson's 73-minute live lecture deriving trigonometry from the unit circle: why sine and cosine are coordinates, where the Pythagorean identity comes from, negative angles, and the half-angle formula, with live audience problems throughout. It derives the unit-circle definitions rather than presenting them as a table to memorize, and the accompanying lesson page at 3blue1brown.com carries the notes and practice problems. F **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.youtube.com/watch?v=yBw67Fb31Cs **Tags:** unit-circle, trigonometry, trigonometric-identities, live-lecture --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/unit-circle