trigonometry

136 GEOMETRY AND TRIGONOMETRY
Figure 13.9
which corresponds to length OA in Fig. 13.9.
y = r sin θ = 4.5 sin 5.16 =−4.057
which corresponds to length AB in Fig. 13.9.
Thus (1.948, −4.057) in Cartesian co-ordinates
corresponds to (4.5, 5.16 rad) in polar
co-ordinates.
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 0x and 0y
in (a) polar form, (b) Cartesian form.
Calculate also the shortest distance between
the centres of two adjacent holes.
y
13.4 Use of R → P and P → R
functions on calculators
Another name for Cartesian co-ordinates is rectangular
co-ordinates. Many scientific notation calculators
possess R → P and P → R functions. The
R is the first letter of the word rectangular and the P is
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.
O
x
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 coordinates
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)]
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]