Embed Size (px)
Citation preview
Trigonometric Robot
Workbook Version 0.1Prepared by Phil Bourke
Tipperary Institute
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.....
Degrees Versus Radians
circumference
diameter
circumference = 2pi*r circumference = 3.14 * r
Degrees Versus Radians
90o
Degrees Versus Radians
90o
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.
Degrees Versus Radians
90o
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 6.28318A 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 90o for a circle of r = 1 is equal to 1.570795 radians.
Degrees Versus Radians
90o
1.570795 radians
The circumference of a circle is 2pi*r.If r=1, then C=2pi*1, or 6.28318A 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 90o for a circle of r = 1 is equal to 1.570795 radians.
Degrees Versus Radians
90o
1.570795 radians
The circumference of a circle is 2pi*r.If r=1, then C=2pi*1, or 6.28318A radian is the proportion of the circumference described by the angle (in radians)Angle(radians)/6.28318 = r/C. An angle of 90o for a circle of r = 1 is equal to 1.570795 radians.
Unit Circle Trigonometry
0,0
0,1
0,-1
1,0-1,0
Sin = Distance XCos = Slope Y
Unit Circle Trigonometry
0,0
0,1
0,-1
1,0-1,0Plotting X
Plotting Y Plot courtesy http://www.ibm.com/developerworks/library/j-robocode2/sidefile-robo2.html
Unit Circle Trigonometry
0,0
0,1
0,-1
1,0-1,0Plotting X
Plotting Y Plot courtesy http://www.ibm.com/developerworks/library/j-robocode2/sidefile-robo2.html
Updated version to follow
