Page 187 - Mathematics_Form_Two

Trigonometry

4. Study the values and record the sin x = 0.5 x =
pattern you have observed from x =
sine, cosine, and tangent values in cos x = 0.5344
the table. tanθ = 1.4071 θ =

5. Justify your reasoning by sin y = 0.834 y =
demonstrating how you have 3sinα = 2 α =
FOR ONLINE READING ONLY
arrived at your answers. cosβ = 2.0784 β =
tan3x = 4.3260 x =
Inverses of trigonometric ratios cosθ = tan 25° θ =

Given a trigonometric ratio, say x, the 3. Explain the process you have used Mathematics for Secondary Schools
corresponding angle can be found using the to arrive at your conclusion.
inverse trigonometric functions, denoted
1
−
1
−
as sin , cos , and tan . For example, Example 8�18
−
1

if cos0° = then cos (1) 0 .= ° It is read If tan x = 1.4071, find the value of x.
1
−
1,
as “the inverse of cosine 1 is zero”. This
applies similarly to other ratios, such as the Solution
inverse of sine and the inverse of tangent. Given tan x = 1.4071, it follows that;
1
−
x = tan (1.4071)
The inverse trigonometric ratios can
°
=
be determined using a calculator, 54 36′
graphical methods, and other Therefore, x = 54º36′.
techniques. Participate in Activity 8.4
to learn how to determine the inverse of Note: The values of sine and cosine of
trigonometric ratios using a calculator. an angle cannot be greater than 1, but
values of tangents of angles can be
Activity 8�4: Determining inverse greater than 1.
trigonometric ratios
using a calculator Example 8�19

1. Explore different sources Find the values of x and y, correct to
including the internet to learn how 3 significant figures in each of the

to use a calculator to determine following figures.
inverse trigonometric ratios. (a)

2. Write all the necessary steps to be
followed and use the knowledge 32 cm
obtained in Task 1 to complete x
the following table.
37º

181
Student's Book Form Two

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MATHEMATIC F2 v5.indd 181 11/10/2024 20:14:09
MATHEMATIC F2 v5.indd 181