Introduction to trigonometry 103
(c) cot−^12. 1273 =tan−^1
(
1
2. 1273
)
=tan−^10. 4700 ...
=25.18◦or 25 ◦ 11 ′
or0.439radians
Problem 18. Evaluate the following expression,
correct to 4 significant figures:
4sec32◦ 10 ′−2cot 15◦ 19 ′
3cosec 63◦ 8 ′tan14◦ 57 ′
By calculator:
sec32◦ 10 ′= 1. 1813 ,cot15◦ 19 ′= 3. 6512
cosec 63◦ 8 ′= 1. 1210 ,tan14◦ 57 ′= 0. 2670
Hence
4sec32◦ 10 ′−2cot15◦ 19 ′
3cosec 63◦ 8 ′tan14◦ 57 ′
=
4 ( 1. 1813 )− 2 ( 3. 6512 )
3 ( 1. 1210 )( 0. 2670 )
=
4. 7252 − 7. 3024
0. 8979
=
− 2. 5772
0. 8979
=−2.870,
correct to 4 significant figures.
Problem 19. Evaluate correct to 4 decimal places:
(a) sec(− 115 ◦) (b) cosec(− 95 ◦ 47 ′)
(a) Positive angles are considered by convention to be
anticlockwise and negative angles as clockwise.
Hence− 115 ◦is actually the same as 245◦(i.e.
360 ◦− 115 ◦)
Hence sec(− 115 ◦)=sec245◦=
1
cos245◦
=−2.3662
(b) cosec(− 95 ◦ 47 ′)=
1
sin
(
− 95
47 ◦
60
)=−1.0051
Problem 20. In triangleEFGin Fig. 11.11,
calculate angleG.
2.30
8.71
F
E
G
Figure 11.11
With reference to∠G, the two sides of the triangle
given are the opposite sideEFand the hypotenuse
EG; hence, sine is used,
i.e. sinG=
2. 30
8. 71
= 0. 26406429 ...
from which, G=sin−^10. 26406429 ...
i.e. G= 15. 311360 ...
Hence, ∠G= 15. 31 ◦or 15 ◦ 19 ′
Now try the following exercise
Exercise 46 Further problemson
evaluating trigonometric ratios
In Problems 1 to 8, evaluate correct to 4 decimal
places:
- (a) sine 27◦ (b) sine 172. 41 ◦
(c) sine 302◦ 52 ′[
(a) 0. 4540 (b) 0. 1321
(c)− 0. 8399
]
- (a) cosine124◦ (b) cosine21. 46 ◦
(c) cosine284◦ (^10) [′
(a)− 0. 5592 (b) 0. 9307
(c) 0. 2447
]
- (a) tangent145◦ (b) tangent310. 59 ◦
(c) tangent49[◦ 16 ′
(a)− 0. 7002 (b)− 1. 1671
(c) 1. 1612
]
- (a) secant 73◦ (b) secant 286. 45 ◦
(c) secant 155◦ (^41) [′
(a) 3. 4203 (b) 3. 5313
(c)− 1. 0974
]