Page 68 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

(ii) The cosine of the an angle is equal to the sine of its complementary angle.
Example 19
(a) Given that sin 25° 5 0.423, without using
tables, determine the value of cos 65°.
(b) Given that cos 25° 5 0.906, without using tables, determine the value of sin 65°.
6Solution
(a) Given that sin 25° 5 0.423
then cos(90° 2 25°) 5 cos65° 5 sin25° 5 0.423
(complementary /s) So the value of cos 65° is 0.423.
(b) Given that cos 25° 5 0.906
then sin (90° 2 25°) 5 sin65° 5 cos25° 5 0.906
sin 21.5° without using tables.
12. If cos 71.8° 5 0.312, determine the value of sin 18.2 without using tables.
ANGLES OF
Angles of Elevation
ELEVATION AND DEPREaSndSDIOepNression
B
Plateau - horizontal plane
A
Road - horizontal plane
InFtihge. 1d1i.a7g7raHmoriazbonotvael pshlaonwes a Person A standing on a horizontal plane (e.g. a road) and a Person B
So
592
Chapter11.indd 592
(complementary /s) the value of sin 65° is 0.906.
Fig 11.77 above shows a Person A standing on a hor- staiznodntianlgpolannean(eo.gth.earrohaodr)izaonndtalPpelrasnoneB(es.gta.nadipnlga-
on another horizontal plane (e.g. a plateau). teau).
Chapter 11
Trigonometry 1
(a)
From what wa
(i) • The ang observer
B
a Angle of elevation
Horizontal line of sight of Person A
11/17/2009
angle for the obser
62
Observer
Fig. 11.78 Angle of elevation
If Person A looks along a horizontal line of sight, then he would not be able to see person B.
If however his line of sight is inclined at the correct angle and he looks upwards, then he would be able to see Person B. The angle formed by Person A’s horizontal line of sight and his inclined line of sight is called the angle of elevation.
(b)
A
Fig. 11.79 Angle of depression
(c)
Horizontal plane
b
For examp
Horizontal line of sight of Person B Angle of depression
B
11:36:42 PM
A
• Or,thea upwards
• Or, the a the line
and the h
For example:
Observer
Fig. 11.81 An The angle of e
B
If Person B looks along a horizontal line of sight, then he would not be able to see Person A.
If however his line of sight is declined at the correct angle and he looks downwards then he would be able to see Person A. The angle formed by Person B’s horizontal line of sight and his declined line of sight is called the angle of depression.
is 40°. (ii) •
•
•
The ang observer angle fo the obse Or, the sured d object. Or, the between downwa
s
l
n f
n
o o
g l
r r
a o
r
Inclined line of sight
b
Declined line of sight
Line of sight
Up Down
a