Unit Circle Project

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* Explain what a radian measure represents using the unit circle as a reference. Pie is represented by a real number constant and is the ratio of the circumference of a circle to its diameter. Its value is approximately 3.14159. Since the circumference of the unit circle is 2 Pie, it is implied that the radian measure of an angle of one revolution is also 2 Pie. So the radian is the measure of how close a degree is to a complete circle. * How do special right triangles directly relate to the unit circle? There are two types of special right triangle, 90, 60, 30 and 45, 45, 90. With both triangles, the angles of degrees are directly related to the x and y values on the unit circle. With the case of 90, 60, 30 and 90, 45, 45, the angles are relative to the sin of its value on the unit circle. For an example, the sin of 30 degree is ½ and the sin of 60 degree is radical 3 over 2. Same with the special right triangle of 90, 45, 45, the sin of 45 is radical 2 over 2. * Suppose that you did not have the unit circle on Circle A, but rather a circle of radius 5. Will the angle measures in degrees and/or radians change? Why or why not? If the radius was to increase to 5, the angle measures will not change regardless. All the sin and cos values change but angle measurement will not be affected. This is because the revolution of a circle will always be 2 pie radians or 360 degree. Angle measures are the same in every circle as they are proportionate. * Suppose that you did not have the unit circle on Circle A, but rather a circle of radius 5. What do you suppose the x- and y- coordinates will be for that circle in Quadrant 1? As we know sin is relative to y and cos is relative to x. With this given, the x and y coordinates for a circle with a radius of 5 would simply be sin=y/radius and cos=x/ radius. This would apply to any circle with different radii.

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