Higher Engineering Mathematics

136 GEOMETRY AND TRIGONOMETRY

Figure 13.9

which corresponds to lengthOAin Fig. 13.9.

y=rsinθ= 4 .5 sin 5. 16 =− 4. 057

which corresponds to lengthABin Fig. 13.9.

Thus (1.948,−4.057) in Cartesian co-ordinates
corresponds to (4.5, 5.16 rad) in polar
co-ordinates.

13.4 Use ofR→PandP→R

functions on calculators

Another name for Cartesian co-ordinates isrect-
angularco-ordinates. Many scientific notation cal-
culators possessR→PandP→Rfunctions. The
Ris the first letter of the word rectangular and thePis
the first letter of the word polar. Check the operation
manual for your particular calculator to determine
how to use these two functions. They make changing
from Cartesian to polar co-ordinates, and vice-versa,
so much quicker and easier.

Now try the following exercise.

Exercise 62 Further problems on changing

polar into Cartesian co-ordinates

In Problems 1 to 8, express the given polar co-

ordinates as Cartesian co-ordinates, correct to

3 decimal places.

1. (5, 75◦) [(1.294, 4.830)]


2. (4.4, 1.12 rad) [(1.917, 3.960)]
   3. (7, 140◦)[(−5.362, 4.500)]
   4. (3.6, 2.5 rad) [(−2.884, 2.154)]
   5. (10.8, 210◦)[(−9.353,−5.400)]
   6. (4, 4 rad) [(−2.615,−3.207)]
   7. (1.5, 300◦) [(0.750,−1.299)]
   8. (6, 5.5 rad) [(4.252,−4.233)]
   9. Figure 13.10 shows 5 equally spaced holes
   on an 80 mm pitch circle diameter. Calculate
   their co-ordinates relative to axes 0xand 0y
   in (a) polar form, (b) Cartesian form.

Calculate also the shortest distance between

the centres of two adjacent holes.

O x

y

Figure 13.10

[(a)40∠ 18 ◦,40∠ 90 ◦,40∠ 162 ◦,

40 ∠ 234 ◦,40∠ 306 ◦,

(b) (38. 04 +j12.36), (0+j40),

(− 38. 04 +j12.36),

(− 23. 51 −j32.36), (23. 51 −j32.36)

47 .02 mm]