The definition of polar coordinates can be given in many forms, one of the easiest way of defining polar coordinates is given below:
Here "O" is the POLE and OB is the polar axis, the distance OA is called the radial coordinate (r) and the angle 600 is called the angular coordinate The radial coordinate is often denoted by r, and the angular coordinate by ? or t .Angles in polar notation are generally expressed in either degrees or radians.
What are the uses of polar coordinates?
The polar coordinates are useful in describing the human body motion since the essence of the human body motion is the joint motions. The segments undergo rotations about the joint centers and using the azimuth angle (while r = const) in describing the body motion is more efficient than using the Cartesian coordinates. One thing to note here is that coordinates r & 0 are not the same kind.
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Lets take an example of converting polar coordinate into cartesian coordinates. The two polar coordinate r and θ can be converted to the Cartesian coordinates x and y by using the trignometric functions sine and cosine:
What is (12,5) in Polar Coordinates?
We use the pythagorean theorem to find the longest side as
r2= 122 + 52
r = √ (122 + 52)
r = √ (144 + 25) = √ (169) = 13
we use the tangent function to find the angle
tan( θ ) = 5 / 12
θ = tan-1( 5 / 12 ) = 22.6 °
so the cartesian coordinate (12,5) in
polar coordinate is (13,22.60 )
r = √ (x2 + y2)
θ = atan( y / x )
|More topics in Polar Coordinates|
|Polar Equations of Lines||Graphing Polar Equations|
|Rectangular to Polar Coordinates||Circle in Polar Coordinates|
|Spherical Coordinates||Parametric Functions|
|Distance Formula for Polar Coordinates|
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