Basic Engineering Mathematics, Fifth Edition

Cartesian and polar co-ordinates 217

Now try the following Practice Exercise

PracticeExercise 95 Changing polar to
Cartesianco-ordinates (answerson
page 350)

In problems 1 to 8, express the given polar co-
ordinates as Cartesian co-ordinates, correct to 3
decimal places.

1. (5, 75◦) 2. (4.4, 1.12rad)


2. (7, 140◦) 4. (3.6, 2.5rad)


3. (10.8, 210◦)6.(4,4rad)


4. (1.5, 300◦) 8. (6, 5.5rad)


5. Figure 24.10 shows 5 equally spaced holes
   on an 80mm pitch circle diameter. Calculate
   their co-ordinates relative to axesOxandOy
   in (a) polar form, (b) Cartesian form.


6. In Figure 24.10, calculate the shortest dis-
   tance between the centres of two adjacent
   holes.

y

O x

Figure 24.10

24.4 Use of Pol/Rec functions on calculators

Another name for Cartesian co-ordinates isrectangular

co-ordinates. Many scientific notation calculators have

PolandRecfunctions. ‘Rec’ is an abbreviationof ‘rect-

angular’ (i.e. Cartesian) and ‘Pol’ is an abbreviation of

‘polar’. Check the operation manual for your particular

calculator to determine how to use these two func-

tions. 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 sim-

ilar, to change the Cartesian number (3, 4) into polar

form, the following procedure is adopted.

1. Press ‘shift’ 2. Press ‘Pol’ 3. Enter 3


2. Enter ‘comma’ (obtained by ‘shift’ then ) )


3. Enter 4 6. Press ) 7. Press=
   The answer isr= 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.


4. Press ‘shift’ 2. Press ‘Rec’


5. Enter 7 4. Enter ‘comma’


6. Enter 126 (assuming your calculator is indegrees
   mode)


7. 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 Practice Exercises 94 and 95 in

this chapter and use your calculator to determine the

answers, and see how much more quickly they may be

obtained.