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A unit circle is a circle with a radius equal to one (1) unit. The circle is portioned into sectors based on the special right triangles 30°-60°-90° and 45°-45°-90°. These are the grey lines within the circle. To see the Degree measures check the Degrees check box. Radian measures use the Radian check box. When you select the Coordinate value, these are the cosine and sine values of the special right triangles 30°-60°-90° and 45°-45°-90°. Use the "tri-" sliders to view how these special right triangles fit on the unit circle. See Unit Circle Triangles for additional information. Select each check box separately to see and learn the values described. Memorize the whole Unit Circle.
Radians measure is determined by the number of radii that lay on the circumference of the circle. The coordinates are the cosine and sine of the angles formed. The cosine is always the x-value laying on the x-axis. The sine is the always the y-value laying on the y-axis. The signs of the coordinate values follow the same rule used by the quadrants of the coordinate system. Finger Mnemonics can help you remember these values. Memory triggers can assist in using function arithmetic. This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers with a worksheet to be complete for a grade.