Chapter 9: Vector Calculus
Section 9.2: Vector Objects
Enter the Cartesian point x,y=1,2 as a free vector, then change to polar coordinates.
The polar coordinates of the Cartesian point x,y=1,2 are
r=x2+y2=12+22=5 and θ=arctany,x=arctan2,1=arctan2
Hence, r,θ=5,arctan2. Note the use of the two-argument arctangent function, which returns an angle in one of the four quadrants. Although it is easier to use for normal manipulations, the one-argument arctangent function, namely, arctany/x returns an angle in either the first or fourth quadrants.
Maple Solution - Interactive
Tools≻Load Package: Student Vector Calculus
Tools≻Tasks≻Browse: Calculus - Vector≻Vector Algebra and Settings≻Display Format for Vectors
Press the Access Settings button and select "Display as Column Vector"
Display Format for Vectors
Enter point as a free vector and change coordinates
Write the given point as a free vector.
Context Panel: Evaluate and Display Inline
Context Panel: Student Vector Calculus≻Conversions≻Change Co-ordinate System
Complete "Specify coordinates" dialog as per Figure 9.2.1(a)
Figure 9.2.1(a) Coordinate-change dialogs
1,2 = 12→change coordinates5arctan⁡2
Maple Solution - Coded
Install the Student VectorCalculus package and execute the BasisFormat command.
Apply the MapToBasis command to the given point
MapToBasis1,2,polarr,θ = 5arctan⁡2
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