Page 175 - Mathematics_Form_Two

Trigonometry

Lengthof adjacent side 0
cos 90°= =
Lengthof hypotenuse side AC
= 0

Therefore, sin 0° 0= .
FOR ONLINE READING ONLY
0 Also,
= = 0, if BC ≠ 0
BC Lengthof adjacent side
Lengthof opposite side cos 0°= Lengthof hypotenuse side
tan 90°=
Lengthof adjacent side AB Mathematics for Secondary Schools
= = 1
BC BC AC
= =
AB AA 0 Therefore, cos 0° = 1.

BC Similarly,
= = undefined
0 tan 0°= Lengthof opposite side
Lengthof adjacent side

Values of sin 0º, cos 0º, and tan 0º = 0

Consider the right-angled triangle in = 0 AB
Figure 8.6.
In this case, the opposite side shrinks to
zero so that the hypotenuse overlaps with
the adjacent side.

Therefore, tan 0° = 0.
The results for all special angles are
summarised in Table 8.1.

Table 8�1: Trigonometric ratios of special angles
x sin x cos x tan x
Figure 8�6: Movement of AC towards AC 0
0º 0 1 0

1 3 3
In Figure 8.6, if AC collapses to AC , 30º 2 2 3
0
ˆ
then RPQ becomes0.° The hypotenuse
CAC

0
and adjacent sides overlap, that is 45º 2 2 2 2 1
AC = AB. This means that the opposite 3 1

side becomes zero, BC CC= 0 = 0. Thus, 60º 2 2 3

Lengthof opposite side 90º 1 0 undefined
sin 0°=
Lengthof hypotenuse side

169
Student's Book Form Two

11/10/2024 20:13:50
MATHEMATIC F2 v5.indd 169 11/10/2024 20:13:50
MATHEMATIC F2 v5.indd 169