Page 174 - Mathematics_Form_Two

Trigonometry

From Figure 8.3, it follows that Using the Pythagoras' theorem, it implies
BD = DC = 1 unit. that, PR = 1 + 2 1 = 2 2 units.
Apply the Pythagoras' theorem:

BD + 2 AD = 2 = 2 AB 2 The following trigonometric ratios are
2
obtained.
2
2
2
1 + AD = 4 1 3−= 2 tan 45º = RQ = = 1,
AD =
FOR ONLINE READING ONLY
PQ
1
0
tan 45
Mathematics for Secondary Schools Thus, the following trigonometric ratios sin 45º = PQ = = 1 1 = = 2 2 2 , .
2
1
AD =
3 units.
PR
2
are obtained.
RQ
cos 45º =
2
PR
2
AD
sin 60
0
sin 60° =
AB = 2 3 , Values of sin 90°, cos 90°, and tan 90°
AD 3
tan 60° = = = 3 , Consider the right-angled triangle ABC in
BD 1 Figure 8.5.
BD 1
cos60
0
cos 60° = = ,
AB 2
BD 1
sin30 =
0
sin 30° = ,
AB 2
BD 1 3
tan30
0
tan 30°= = = ,
AD 3 3
AD 3
cos30
0
cos 30°= = . Figure 8�5: Trigonometric ratios of angle 90°
AB 2
In Figure 8.5, if AC approaches A C,
0
ˆ
Consider an isosceles triangle PQR in then CAA approaches 90°. The
0
Figure 8.4 in which the base angle is 45° hypotenuse side AC and the opposite
and PQ = RQ 1= unit. side BC overlap so that AC = BC. Also,

O.
the adjacent side AB AA= 0 =0. Thus,
Lengthof opposite side
sin90°= .
Lengthof hypotenuse side
BC BC
= =
Figure 8�4: Isosceles triangle with special AC BC
angle measuring 45° 1=

168
Student's Book Form Two

11/10/2024 20:13:49
MATHEMATIC F2 v5.indd 168
MATHEMATIC F2 v5.indd 168 11/10/2024 20:13:49