Page 168 - Mathematics_Form_Two

Trigonometry

Consider the right-angled triangle ABC BC DE GF
shown in Figure 8.1. Similarly, = = = , s
AC AE AF
where s is a constant ratio. This constant
ratio is called the sine of the angle at the
vertex A and is written in short a sinA.
FOR ONLINE READING ONLY
Mathematics for Secondary Schools Figure 8�1: Right-angled triangle ABC Likewise, AC = AE = AF = , n
AB
BA
AG
AD
c,
AC
where c is a constant ratio. This constant
ratio is called the cosine of the angle at
vertex A and is written in short as cosA.

From ∆ABC, in Figure 8.1, CÂB = x, From Figure 8.1 and 8.2, it can be
AB and AC. is the lenght of the hypotenuse side, deduced that, the lengths of the sides of a
is the length right-angled triangle are used to define the
with respect to angle x, AB and AC.
of adjacent side, and BC is the length of trigonometric ratios as follows:
opposite side.
Length of oppositeside BC
Consider similar triangles shown in Figure tanA= =
8.2. Length of adjacentside AB
Length of oppositeside BC
sinA= =
Length of hypotenuse side AC

Length of adjacent side AB
cosA= =
Length of hypotenuse side AC

The following mnemonic is a useful way
of remembering these definitions.
Figure 8�2 Similar triangles
SO TO CA
From Figure 8.2, since the triangles are H A H
similar, it follows that
Using the mnemonic, it follows that,
O
CB = ED = FG = , r t, S = is a definition of sin A,
AB AD AG H
O
where t is a constant ratio. This constant T = is a definition of tan A,
A
ratio is called the tangent of the angle
A
at the vertex A and is written in short as C = is a definition of cos A.

tanA. H

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Student's Book Form Two

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