Page 173 - Mathematics_Form_Two

Trigonometry

1 relationship between the ratios
0
sin 30
8. Given that sin 30º = , find the of different angles.
value of cos 30º. 2
9. In a triangle ABC, AB = c, (c) Find the values of
2
2
ˆ
BC = a, AC = b, and ABC 90= = 90º. sin A cos A+ 2 and
0
and make
2
sin B cos B+

Find in terms of a, b or c each of a conclusion about these
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the following: relationships.
(a) sin C (b) cos C (c) tan C
15. In the following figure, evaluate
sin C
(d) cos C sin x + tan .y Mathematics for Secondary Schools
(e) The relationship between tan C
sin C
and
cos C
10. In a right-angled triangle, the length
of the hypotenuse is 10 cm and one

of its angles is 70 .° Calculate the
length of the shortest side Trigonometric ratios of special
=
(use cos 70° 0.342). angles
11. In a right-angled triangle, the Special angles are angles whose
tangent of one of the acute angles is trigonometric ratios can be found by using
1. How are the measures of the two simple ratios. The special angles are 30º,
legs related to each other? 45º, 60º, and 90°.
Consider the equilateral triangle ABC in
12. If α is an acute angle and Figure 8.3. Let the length of each side be
sinα = 0.75, find the values of 2 units. The altitude from vertex A bisects
cosα and tan .α BC at D.

4
13. Given that sinθ = , find the values
9

of cosθ and tanθ .
14. In a right-angled triangle ACB,
AĈB = 90°, AC = 4 cm,

and BC 3 cm.=
(a) How are the angles A and B
related?
(b) Find the value of sin A, cos A, Figure 8�3: A triangle with special angles 30°
sin B, cos B and deduce the and 60°

167
Student's Book Form Two

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MATHEMATIC F2 v5.indd 167