Page 179 - Mathematics_Form_Two

Trigonometry

Trigonometric ratios of any angle 9. Comment on the results obtained in

To understand trigonometric ratios of tasks 6 and 8.
any angle, it is important to go beyond 10. Share your observations on the
right-angled triangles. By using the unit relevance of the relationship
circle and the Cartesian coordinate system, between angles and sides of a right-
these ratios can be defined for any angle, angled triangle.
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making it easier to explore relationships
between angles. Consider a circle of unit radius subdivided
into four congruent sectors by the
Activity 8�2: Introducing the relationship coordinate axes whose origin is at the Mathematics for Secondary Schools
of sides, lengths, and centre of the circle as shown in Figure 8.7.
angles of a triangle
1. Using a scale, draw three right-angled
triangles PQR, ABC, and MNT
such that PQ = 4cm , QR = 3 cm,

PR = 5cm , AB = 8cm , BC = 15cm
AC = 17cm , MN = 6cm ,
MN
NT = 8cm , and MT = 10 cm.

PQ AB MN
2. Calculate , , and .
PR AC MT
MN
QR BC MN Figure 8�7: An acute angle in a unit circle
NT
3. Calculate , , and .
PR AC MT Let θ be any acute angle 0°<θ <90°)
(
PQ AB MN located in the first quadrant and P be a
4. Calculate , , and .
CB
QR BC NT point on the circle with coordinates (x, y),
where OP is the radius of the unit circle.
!
5. Use a protractor to measure PRQ , The trigonometric ratios in this circle

!
!
ACB, and MTN . can be obtained by using the sides of a

6. Calculate the values of sine, cosine right-angled triangle OPQ as follows:
and tangent of angles in task 5 and
compare the results with the ratios QP y ,
in tasks 2, 3, and 4, respectively. sinθ = OP = 1 = y
!
7. Use a protractor to measure BAC , cosθ = OQ = x =

!
!
QPR , and NMT . OP 1 x ,
8. Repeat task 6 using the angles QP y
obtained in task 7. tanθ = OQ = x .

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Student's Book Form Two

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