Wednesday, February 6, 2013

Graphing Calculator Polar Coordinates

In this article, we are going to study about graphing calculator polar coordinates. It is very simple to work on the polar coordinates graphing calculator. For example, if we want to graphing radians r = 3 and `theta=45^o` on the polar graph paper, we have to just enter `3` in the radians text box and `45^o` in angles in degrees text box and then click the enter button, Now the calculator automatically plot the polar coordinates on the display of the polar graph paper. These process are shown in the below figure.

Graphing calculator polar coordinates


Graphing Calculator Polar Coordinates - Example 1:

Study and graphing of the given polar coordinates.

(2, 50o), (3, 210o), and (-2, 135o).

Solution:

Graphing the given polar coordinates are on the below polar graph paper:

Graphing calculator polar coordinates

Steps for plotting polar coordinates (2, 50o):

1:   The radian 2 is marked from the origin (pole) on the positive side of the x axis.

2:   The given angle 50o is rotated in anticlockwise directions and then plot the required polar coordinates (2, 50o) as shown in figure.

Steps for plotting polar coordinates (3, 210o):

1:   The radian 3 is marked from the origin (pole) on the positive side of the x axis.

2:   The given angle 210o is rotated in counterclockwise directions and then plot the polar coordinate (3, 210o) as shown in figure.

Steps for plotting negative polar coordinates (-2, 135o):

1:   The radian 2 is marked from the origin on the positive side of the x axis.

2:   The given angle 135o , is rotated in anticlockwise directions and it is determined.

3:   Now we can extend the 135o degree line in opposite direction (315o) where we get  the radian 2 in negative sign and then plot the polar coordinates (-2, 135o).

Graphing Calculator Polar Coordinates - Example 2:

Study and graphing of the given polar coordinates by using the above calculator.

(2.5, 60o), (-1, 75o), and (3, -30o).

Solution:
Polar coordinates are on the below polar graph paper:

Graphing calculator polar coordinates

Steps for plotting polar coordinates (2.5, 60o):

Step 1:   The radian 2.5 is marked from the origin (pole) on the positive side of the x axis.

Step 2:   The given angle 60o is rotated in anticlockwise directions and then plot the required polar coordinates (2,.5 60o) as shown in figure.

Steps for plotting polar coordinates (3, -30o):

Step 1:   The radian 3 is marked from the origin (pole) on the positive side of the x axis.

Step 2:   The given angle 30o is rotated in clockwise directions and then plot the polar coordinate (3, -30o) as shown in figure.

Steps for plotting negative polar coordinates (-1, 75o):

Step 1:   The radian 1 is marked from the origin on the positive side of the x axis.

Step 2:   The given angle 75o , is rotated in anticlockwise directions and it is determined.

Step 3:   Now we can extend the 75o degree line in opposite direction (255o) where we get  the radian 1 in negative sign and then plot the polar coordinates (-1, 75o).

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