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Unit circle
In trigonometry, the unit circle has a radius of 1 and is centered at the origin. It’s useful for learning ratios like sine and cosine. It also illustrates the relationship between angles in degrees and radians.
See also:Wikipedia · Math is Fun
LoadingHow to solve for (x, y) coordinates
Select an angle abovex = cos(θ)y = sin(θ)
Selected angle: θ = 0° = 0 radiansx = cos(θ) = cos(0) = 1y = sin(θ) = sin(0) = 0
Selected angle: θ = 30° = π over 6 radiansx = cos(θ) = cos(π over 6) = root 3 over 2y = sin(θ) = sin(π over 6) = 1 over 2
Selected angle: θ = 45° = π over 4 radiansx = cos(θ) = cos(π over 4) = root 2 over 2y = sin(θ) = sin(π over 4) = root 2 over 2
Selected angle: θ = 60° = π over 3 radiansx = cos(θ) = cos(π over 3) = 1 over 2y = sin(θ) = sin(π over 3) = root 3 over 2
Selected angle: θ = 90° = π over 2 radiansx = cos(θ) = cos(π over 2) = 0y = sin(θ) = sin(π over 2) = 1
Selected angle: θ = 120° = 2π over 3 radiansx = cos(θ) = cos(2π over 3) = negative 1 over 2y = sin(θ) = sin(2π over 3) = root 3 over 2
Selected angle: θ = 135° = 3π over 4 radiansx = cos(θ) = cos(3π over 4) = negative root 2 over 2y = sin(θ) = sin(3π over 4) = root 2 over 2
Selected angle: θ = 150° = 5π over 6 radiansx = cos(θ) = cos(5π over 6) = negative root 3 over 2y = sin(θ) = sin(5π over 6) = 1 over 2
Selected angle: θ = 180° = π radiansx = cos(θ) = cos(π) = negative 1y = sin(θ) = sin(π) = 0
Selected angle: θ = 210° = 7π over 6 radiansx = cos(θ) = cos(7π over 6) = negative root 3 over 2y = sin(θ) = sin(7π over 6) = negative 1 over 2
Selected angle: θ = 225° = 5π over 4 radiansx = cos(θ) = cos(5π over 4) = negative root 2 over 2y = sin(θ) = sin(5π over 4) = negative root 2 over 2
Selected angle: θ = 240° = 4π over 3 radiansx = cos(θ) = cos(4π over 3) = negative 1 over 2y = sin(θ) = sin(4π over 3) = negative root 3 over 2
Selected angle: θ = 270° = 3π over 2 radiansx = cos(θ) = cos(3π over 2) = 0y = sin(θ) = sin(3π over 2) = negative 1
Selected angle: θ = 300° = 5π over 3 radiansx = cos(θ) = cos(5π over 3) = 1 over 2y = sin(θ) = sin(5π over 3) = negative root 3 over 2
Selected angle: θ = 315° = 7π over 4 radiansx = cos(θ) = cos(7π over 4) = root 2 over 2y = sin(θ) = sin(7π over 4) = negative root 2 over 2
Selected angle: θ = 330° = 11π over 6 radiansx = cos(θ) = cos(11π over 6) = root 3 over 2y = sin(θ) = sin(11π over 6) = negative 1 over 2
Selected angle: θ = 360° = 2π radiansx = cos(θ) = cos(2π) = 1y = sin(θ) = sin(2π) = 0
Interactive Unit Circle - Math is Fun
Sine, Cosine and Tangent ... in a Circle or on a Graph. ... Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle Interactive …
See results only from mathsisfun.comUnit Circle
The "Unit Circle" is a circle with a radius of 1. Being so simple, it is a great way to learn and talk about lengths and angles. The center is put on a gr…
Interactive Unit Circle – GeoGebra
An interactive for exploring the coordinates and angles of the unit circle, as well as finding the patterns among both.
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Unit Circle - Desmos
Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Interactive Unit Circle v1.01 - Desmos
Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Unit Circle - GeoGebra
Interactive Unit Circle. Activity. J Rothman. Quiz 1: Trigonometric Functions of Special Angles. Activity. Tim Brzezinski. Unit Circle to Sine and Cosine Functions. Activity. Tim Brzezinski. Trig Reference Circle (2): Choose Your Own Radius. …
Unit Circle Visualizer and Calculator | Learn Math Class
Interactive unit circle visualization tool. Calculate and visualize sine, cosine, tangent and other trigonometric functions in real-time.
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Exploration: Interactive Unit Circle - GeoGebra
An interactive for exploring the coordinates and angles of the unit circle, as well as finding the patterns among both. Explore the unit circle by moving the block dot around the unit circle. After exploring, answer the questions below the unit …
Unit circle
Unit circle or interactive Trigonometric circle helps to see the essence of trigonometric functions sine, cosine, tangent, cotangent, secant, cosecant. It can be customized and rotated with one …
Interactive Unit Circle - Math The Beautiful
Sep 17, 2021 · The unit circle makes things easier, not harder. The unit circle is simple, it's a circle with a radius of 1. So why is it so useful? We can see things in their simplest form. Let's get an intuition of the unit circle by using the …
Interactive Unit Circle - Desmos - MathsLinks
Feb 23, 2023 · The Unit Circle is typically a tool students learn to use when they begin memorizing certain trigonometric ratios and special right triangles. Sometimes teachers will give a mnemonic device for when sine or some other …
Unit Circle Visualizer - GitHub Pages
Welcome to the Trigonometry Visualizer. This tool is meant to give a geometric representation to trigonometric functions. Domain and range are restricted to the Unit Circle. Use "QWERTY" …
Interactive Unit Circle - Math is Fun
images/circle-unit.js Sine, Cosine and Tangent Sine , Cosine and Tangent (often shortened to sin , cos and tan ) are each a ratio of sides of a right angled triangle:
Interactive Unit Circle - GeoGebra
This is an interactive unit circle. You can use the slider in the top left corner to define your angle, which is displayed in both degrees (to the right of the slider) and radians (to the left of the slider).
Unit Circle Game -Interactive quiz on unit circle, radians, degrees ...
Interactive game on all parts of the unit circle, angles, radians, degrees
Unit Circle - Math is Fun
The "Unit Circle" is a circle with a radius of 1. Being so simple, it is a great way to learn and talk about lengths and angles. The center is put on a graph where the x axis and y axis cross, so …
Interactive Unit Circle - Desmos
Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Interactive Unit Circle v1.02 - Desmos
Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
Sine, Cosine, Tangent Unit Circle Interactive Graphs Applet and …
Interactive Trig Graphs and Downloadable Gif Sine, Cosine, Tangent Graphs and the Unit Circle
The Unit Circle | Cambridge (CIE) O Level Additional Maths …
Dec 24, 2024 · The Unit Circle What is the unit circle? The unit circle is a circle with radius 1 and centre (0, 0) The unit circle can be used to explain how trig functions work with angles that are …
5 Unit Circle Tips - wrdsclassroom.wharton.upenn.edu
1 day ago · By applying the 5 unit circle tips outlined in this article, you can improve your skills and confidence in working with this essential concept. Remember to memorize the unit circle, use …
Interactive Unit Circle - GeoGebra
An interactive for exploring the coordinates and angles of the unit circle, as well as finding the patterns among both.
Unit Circle interactive - Desmos
Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
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