100 Higher Engineering Mathematics
B
A
0 2 4
(a)
(b)
68
8
f(x)
7 6 4 3 2 B
A C
0 2 468
8
f(x)
6
4
2
Figure 11.8
Now try the following exercise
Exercise 45 Further problems on
trigonometric ratios of acute angles
- In triangleABC shown in Fig. 11.9, find
sinA,cosA,tanA,sinB,cosBand tanB.
⎡
⎣
sinA=^35 ,cosA=^45 ,tanA=^34
sinB=^45 ,cosB=^35 ,tanB=^43
⎤
⎦
B
C
(^53)
A
Figure 11.9
- If cosA=
15
17
find sinAand tanA, in fraction
form.
[
sinA=
8
17
,tanA=
8
15
]
- For the right-angled triangle shown in
Fig. 11.10, find:
(a) sinα (b) cosθ (c) tanθ
[
(a)
15
17
(b)
15
17
(c)
8
15
]
17
8
15
Figure 11.10
- PointPlies at co-ordinate (−3, 1) and point
Qat (5,−4). Determine
(a) the distancePQ
(b) the gradient of the straight linePQand
(c) the anglePQmakes with the horizontal.
[(a) 9.434 (b)− 0 .625 (c) 32◦]
11.4 Evaluating trigonometric ratios
The easiest method of evaluating trigonometric func-
tions of any angle is by using acalculator.
The following values, correct to 4 decimal places,
may be checked:
sine 18◦= 0 .3090, cosine 56◦= 0. 5592
sine 172◦= 0. 1392 cosine 115◦=− 0 .4226,
sine 241. 63 ◦=− 0 .8799, cosine 331. 78 ◦= 0. 8811
tangent 29◦= 0 .5543,
tangent 178◦=− 0. 0349
tangent 296. 42 ◦=− 2. 0127
To evaluate, say, sine 42◦ 23 ′ using a calculator
means finding sine42
23 ◦
60
since there are 60 minutes
in1degree.
23
60
= 0. 383 3 thus 42 ̇ ◦ 23 ′= 42. 383 ̇◦
Thus sine 42◦ 23 ′=sine 42. 383 ̇◦= 0 .6741, correct to 4
decimal places.
Similarly, cosine72◦ 38 ′=cosine72
38 ◦
60
=0.2985,
correct to 4 decimal places.
Most calculators contain only sine, cosine and tan-
gent functions. Thus to evaluate secants, cosecants and
cotangents, reciprocals need to be used. The following