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Trigonometric Robot Workbook Version 0.1 Prepared by Phil Bourke Tipperary Institute

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Degrees Versus Radians A circle is a shape with all points the same distance from the centre. If you measure the distance around a circle and divide it by the distance across the circle through the centre, you will always come close a value 3.14.....

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Degrees Versus Radians circumference diameter circumference = 2pi*r circumference = 3.14 * r

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Degrees Versus Radians 90 o

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Degrees Versus Radians 90 o What is the ‘circumference distance’ between these points ? Radians Angles can be expressed as radians. Radians are directly proportional to the radius of a circle and the value of pi. By using radians, it is no longer necessary to compute an arc using 3.14.... to infinity. Trigonometric functions (sin, cos, tan etc.) calculations are simplified when angles are expressed in radians.

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Degrees Versus Radians 90 o What is the ‘circumference distance’ between these points ? Radians The circumference of a circle is 2pi*r. If r=1, then C=2pi*1, or 6.28318 A radian is the proportion of the circumference described by the angle (in radians) Angle(radians)/6.28318 = r/C. If the radius of a circle known, the length of any arc can be calculated without using pi. A circle with radius 10 has a circumference of (6.28318 * 5) = 62.8318. So an angle of 90 o for a circle of r = 1 is equal to 1.570795 radians.

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Degrees Versus Radians 90 o 1.570795 radians The circumference of a circle is 2pi*r. If r=1, then C=2pi*1, or 6.28318 A radian is the proportion of the circumference described by the angle (in radians) Angle(radians)/6.28318 = r/C. If the radius of a circle known, the length of any arc can be calculated without using pi. A circle with radius 10 has a circumference of (6.28318 * 5) = 62.8318. An angle of 90 o for a circle of r = 1 is equal to 1.570795 radians.

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Degrees Versus Radians 90 o 1.570795 radians The circumference of a circle is 2pi*r. If r=1, then C=2pi*1, or 6.28318 A radian is the proportion of the circumference described by the angle (in radians) Angle(radians)/6.28318 = r/C. An angle of 90 o for a circle of r = 1 is equal to 1.570795 radians.

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Unit Circle Trigonometry 0,0 0,1 0,-1 1,0 -1,0 Sin = Distance X Cos = Slope Y

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Unit Circle Trigonometry 0,0 0,1 0,-1 1,0 -1,0 Plotting X Plotting Y Plot courtesy http://www.ibm.com/developerworks/library/j-robocode2/sidefile-robo2.html

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Unit Circle Trigonometry 0,0 0,1 0,-1 1,0 -1,0 Plotting X Plotting Y Plot courtesy http://www.ibm.com/developerworks/library/j-robocode2/sidefile-robo2.html

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Chapter 4: Circular Functions Lesson 1: Measures of Angles and Rotations Mrs. Parziale.

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