Cartesian and polar co-ordinates 121
two functions. They make changing from Cartesian to
polar co-ordinates, and vice-versa, so much quicker and
easier.
For example, with the Casio fx-83ES calculator, or
similar, to change the Cartesian number (3, 4) into polar
form, the following procedure is adopted:
- Press ‘shift’ 2. Press ‘Pol’ 3. Enter 3
- Enter ‘comma’ (obtained by ‘shift’ then ))
- Enter 4 6. Press )
- Press= The answer is:r= 5 ,θ= 53. 13 ◦
Hence, (3, 4) in Cartesian form is the same as
(5,53.13◦) in polar form.
If the angle is required inradians, then before repeating
the above procedure press ‘shift’, ‘mode’ and then 4 to
change your calculator to radian mode.
Similarly, to change the polar form number
(7, 126◦) into Cartesian or rectangular form, adopt the
following procedure:- Press ‘shift’ 2. Press ‘Rec’ 3. Enter 7
- Enter ‘comma’
- Enter 126 (assuming your calculator is in
degrees mode) - Press ) 7. Press=
The answer is: X=− 4 .11, and scrolling across,
Y= 5. 66 , correct to 2 decimal places.
Hence, (7, 126◦) in polar form is the same as
(−4.11,5.66) in rectangular or Cartesian form.
Now return to Exercises 53 and 54 in this chapter and
use your calculator to determine the answers, and see
how much more quickly they may be obtained.