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Why do we get the coordinates of a unit circle - Free math help - Live lessons

2,329 views · Published 6 January 2012 · 4:12 · Indexed 6 November 2026

Channel: Brian McLogan · 2012 · Education

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👉 Learn about the points on the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0), (0, 1), (-1, 0) and (0, -1). 

There are other points which are necessary to master in the unit circle. These points can be easily identified using the special triangles. A triangle is drawn in the cartesian plane such that the reference angle is at the origin, the positive or negative x-axis represents the point adjacent to the reference angle, and a line parallel to the positive or negative y-axis represents the opposite of the reference angle.

Recall that a special right triangle is a right triangle with the angles 30, 60, 90 degrees or 45, 45, 90 degrees. Also recall that the ratio of the sides of a special triangle as 1, sqrt(3), 2 respectively for the sides opposite the 30, 60, 90 degrees special triangle and 1, 1, sqrt(2) respectively for the sides opposite the 45, 45, 90 degrees special triangle. The points on the unit circle are easily obtained by dividing the legs of the special triangles by the hypothenuse with the leg adjacent to the reference angle as the x-coordinate and the leg opposite the reference angle as the y-coordinate.

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Organized Videos:
✅ Trigonometric Functions and The Unit Circle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMq-ewwuWUiJyi25hWmFU9rk
✅ The Unit Circle | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpUvFiTSX9I1Qmknmi9fwTh
✅ Points of the Unit Circle | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrIfSXnL_vFq0ZbO-eo6Ux5
✅ Angles of the Unit Circle | Learn About
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMpFziLOs4DgfLlLwewTVGgC
✅ Trigonometric Functions of the Unit Circle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrfrvBwDY-HIKCv-4FgvAD5
✅ Find the Point on the Unit Circle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrRckk3lX1hLafHZcCABVLj
✅ Evaluate Trigonometric Functions Using the Unit Circle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoXRpXt9qSYMjdVA7Rj3KF5
✅ Evaluate the Six Trigonometric Functions Given and Angle
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp1KREwvQxAEe2alDuMTSXO
✅ Evaluate trigonometric functions using a calculator
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMra7ZjRcMsqpwPKjdnLX-rj
✅ Evaluate trigonometric functions using identities
https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMp-xG1q6DJpZlNeRC4n7hYd

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