Unit Circle Game

The unit circle is one of the tools in trigonometry. It is a circle with a radius of 1 centered at the origin (0,0) of a coordinate plane. Because the radius (r) is 1, the coordinates of any point (x, y) on the edge of the circle directly tell you the cosine and sine of the angle θ:
x = cos(θ)
y = sin(θ)

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Unit Circle Quiz/Game
This Unit Circle Master game is a high-speed educational tool designed to help you memorize the unit circle. It tests your ability to quickly identify the exact values of trigonometric functions (sine, cosine, and tangent) for special angles for the four quadrants. Scroll down the page for a more detailed explanation.

Pre-Game Setup
Before clicking Start Challenge, you can customize your experience:
Angle Format: Choose between Degrees (30°, 45°, etc.) or Radians (\(\frac{\pi}{6}, \frac{\pi}{4}\), etc.).
Timer (1m): Toggle this on for a 60-second “blitz” mode. If the timer runs out, the game ends and shows your final score.
Sound: Toggle the audio feedback. Correct answers produce a high “ping,” while wrong answers produce a low “buzz."
How to Play
Once you start, the game presents a series of mathematical problems:
Read the Problem: A trig function and an angle will appear in large text (e.g., \(\sin(\frac{2\pi}{3})\)).
Select the Answer: Four buttons will appear with different simplified radical values. Click the one you believe is correct.
Feedback:
Green: If you are right, the button turns green and you hear a success tone.
Red: If you are wrong, your choice turns red, and the correct answer is highlighted in green so you can learn from the mistake.
Advance: Click the Next Question ➜ button to generate a new problem.
Scoring and Content
The game tracks your progress in the top-left corner (Score: Correct / Total Attempts). The questions cover the entire unit circle.

unit circle (radians)

Have a look at the following lesson on various tricks to remember the unit circle.
How to remember the unit circle?

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