Page 170 - Mathematics_Form_Two

Trigonometry

Example 8�3 BC 4cm
= =
In a right-angled triangle ABC, AB 3cm
4
AB 3cm,= BC = 4cm,and AC 5cm.= Therefore, tanA = 3 .

Find the value of each of the following: Example 8�4
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tan A
(a) sin A
cos A
(b)
(c)
Mathematics for Secondary Schools Solution In a triangle PQR, angle PQR is a right- ;
2 cm,
angle. If RP =
4 cm and PQ =
The given information is summarized in
find the value of each of the following:
the following figure.
(a) QR (b) tan R (c) cos R
Solution
Consider the following figure.

From the figure, triangle ABC is a right-
ˆ
angled triangle such that, ABC = 90°.
It follows that: (a) Apply the Pythagoras theorem as
length of opposite side
opposite side
opposite side
(a) sin A=
ˆ ˆ
(a) sin A =
(a) sin A = length of hypotenuse side follows:
hypotenuse side
hypotenuse side
BC
= BC = = 4 4 4 cm
=
AC
AC 5 5 5 cm
4
ˆ
Therefore, sin A = 4 .
ˆ
Therefore, sin A
Therefore, sin A = = 5 .
5
length of adjacent side
adjacent side
ˆ
(b) cosA
(b) cos A = = length of hypotenuse side (b) tanR= Length of opposite side
Length of adjacent side
hypotenuse side
AB 3 3 cm PQ
=
= =
AC 5 5 cm QR
3 2cm 1
Therefore, cosA = . = =
5 2 3cm 3

(c) tan A= length of opposite side Therefore, tan R = 3 .
length of adjacent side 3
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Student's Book Form Two
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MATHEMATIC F2 v5.indd 164 11/10/2024 20:13:42
MATHEMATIC F2 v5.indd 164