Pol() function only shows the value of r, but not angle theta

Since this calculator cannot perform symbolic manipulations (algebra) you never need to type in sin(theta) or cos(theta). To calculate the sine of an angle (whatever the name of the angle may be) just press the sin key followed by an angle value and the function will be calculated. same thing with any other trigonometric function.
Make sure that the angle units is set to the unit required by your calculation: degree, radian, or grad.

You can create two-element lists and store the results in them.
Create a list L1 with dimension 2

Calculate the Polar coordinates of the point (1,1);: just an example


The 1st element of List 1 is the radius, and the second element is the angle (in radians). Convert it to degrees if you wish. I won't do it.
Now you must extract each element and store it in the r, and theta variables, [ALPHA][x^2] (r) and [ ALPHA] [^] (Theta)
Extract radius and store in r. Extract angle and store in Theta.


To store the rectangular coordinates (x,y) do the same as above. I will leave this pleasure to you.
Note: I inserted screen captures from my calculator but I am not sure if the Parser will accept them. If it does not I will create an image file and insert it as media.

To calculate the Cosine of an angle, you first make sure that the angle unit on your calculator is set to the correct one (degree, or radian). After that it is all simple. Enter the angle value (50 degrees) then press the [COS] key. If you get an error then press the COS key followed by the angle value then press =.
Note if your calculator display Cos ( , with a left parenthesis, then you have to press COS first followed by the angle value and possibly the right parenthesis.
Note. The theta here is of no relevance.

Convert the Cartesian coordinates to polar coordinates (r, Theta). The calculator can do that. Press the SHIFT [+] key combination. Calculator will display Pol(. Type in the Cartesian coordinates (x,y), close the right parenthesis and press [=]. The calculator will display the radius r and the angle theta.
If you want to convert from polar to Cartesian coordinates, use the SHIFT [-] (Rec) key combination. Enter the radius and the angle separated by a comma, close the right parenthesis and press [=]
Be careful, the angle unit you use (radian or degree) will affect the result.

The Pol function converts coordinates from rectangular to polar. Pol(x,y) converts the rectangular coordinates (x,y) to polar coordinates (r, theta).

For examples and instructions, see page E-37 of the manual and example #036 in the Appendix.

No, your calculator does not know a variable called theta. But what is theta but a symbol to represent a variable. Usually it is used to represent an angle in polar coordinates. It is just the usage and it is not really essential. You can do conversion from polar to rectangular coordinates and from rectangular to polar coordinates but it does not matter what the angle variable is called.
Go ahead, do all the calculations you want that involve an angle. If the calculator can perform them , they will be evaluated correctly and the name you give the angle value (alpha, beta, theta, iota...) is immaterial.

See image below

Before graphing deactivate the statistical plots: Press [2nd][Y=] to access the (STAT PLOTS) configuration screen and press [4:PlotsOff][ENTER]

To draw polar graph, make sure in MODE, POL is highlighted.
Make sure that the angle unit is set to RADIAN
If you want the angle unit to be in degrees you must open the WINDOW editor to modify the values of Theta max to a significant value: 30, 45, 60, 90, 120, 180, 360, otherwise the calculator will take the default value 6.28 (2*PI) in degrees

how can i enter a polar form number with angle to convert into a complex numbe(a+bi)

Hello,

Your calculator can draw different kinds of graphics ( Functions, Parametric, Polar, and Sequences).

Apparently, yours is configured to draw in Polar mode, where the variables are named r, the radius, and Theta (a horizontaly barred O) the angle .

To draw the usual y=f(x) graphics,
Press the MODE key/button then look for the 4th line that displays Func, Par, Pol, Seq
Use the left arrow to highlight Func. It will blink. Press ENTER to validate your choice.

After that, Press 2nd MODE and you will get back to the calculation screen.

Then you Press key Y= and start keying in the desired function.

Hope it helps