Page 171 - Mathematics_Form_Two

Trigonometry

Length of adjacent side Example 8�6
(c) cosR =
Length of hypotenuse side
If XYZ is a triangle such that
ˆ
ˆ
= adjacent side

ˆ
(c) cosR = QR = 2 3 cm XYZ = 90 ,° ZY= 5 cm, ZXY = 30 and ZX = 10 cm.°, and
4 cm
PR
hypotenuse side ˆ , find the value of sin30°.
ZY= 5 cm, ZXY = 30 and ZX = 10 cm.°
FOR ONLINE READING ONLY
2 3
= QR = 3 Solution
=
PR 4 2
3 Consider the following figure. From the
Therefore, cosR = . figure, it implies that that
2 Mathematics for Secondary Schools
Example 8�5
5
If tan x = , , find the value of cos .x
12

Solution
5
By definition, tan x = can be ZY
12 sin30° =
represented as shown in the following ZX
triangle. 5cm
= = 0.5
10cm
Therefore, sin 30° = 0.5.

Example 8�7

Use the information provided in the
following figure to calculate the value
of cosx +sin y.

Using Pythagoras’ theorem, the length of
the hypotenuse side is given by;

12 + 2 AC5 = 2 144 25+ = 169 13=

12 + 2 5 = 2 144 25+ = 169 13= units.

AB 12 Solution
Thus, cos x = =
AC 13 From ∆ABC, apply the Pythagoras

12 theorem as follows:
Therefore, cos x = .
13 17 = (BC) + 8 2
2
2

165
Student's Book Form Two

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MATHEMATIC F2 v5.indd 165 11/10/2024 20:13:43
MATHEMATIC F2 v5.indd 165