Page 185 - Mathematics_Form_Two

Trigonometry

Since θ is acute, it follows that Example 8�17

65 65 If sinq = 0.9397 and cosq = 0.3420 ,
cosθ andcosθ = = −
9 9 without using a calculator find the value
sinqsinq 44 6565 4 654 65
tan
tan q = q = == ÷ ÷ ÷ == of tan θ.
cosqcosq 99 99 6565
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Solution
Therefore, and Given sin θ = 0.9397 and

cosθ = 0.3420
Example 8�16 sinq

Given that ∝ and β are complementary From, tanq = cosq . Mathematics for Secondary Schools
angles and sina = 5 , find tan b . 0.9397
13 =
Solution 0.3420

Since ∝ and β are complementary = 2.748
angles, it implies that Therefore, tanq = 2.748 .
∝ + β = 90°

∝ = 90° – β. Exercise 8�4

Hence, sin ∝ = cos(90° − ∝) Without using calculators, answer the
5 following questions:
sina = cos(90° ) cos b- a = = .
13 1. Given that , find the value
But sin b 2 1 cos- 2 . b = of sinθ.

25 2 144 2
b =1-
2
sin b = 1 cos- 169 = 169 2. If tan ∝= 5 , find the value of
25 144 sin (90° − ).
∝
= 1- =
169 169 3. If ∝ and β are complementary angles
12 6
Thus, sin β = ± . Since β is an acute and tan ∝= , find the value of
13 3
12 12
angle, then sin β . and sin β = ≠− tan β.
13 13 4. If sin A = 0.9733 and cos A = 0.2250,

sin b
Hence, tan b = cos b find the value of tan A.
12 5 5. Given that cos θ = 0.9272 and
tanβ = 13 ÷ 13 . tan θ = 0.4040. Find the value of

12 5 12 sin θ.
= ÷ = 3
13 13
5 6. If tanq = 4 , find the value of sin θ.
12
Therefore, tan b = . 7. Given that tan θ = 0.75, find the
5 value of cos θ.

179
Student's Book Form Two

11/10/2024 20:14:07
MATHEMATIC F2 v5.indd 179
MATHEMATIC F2 v5.indd 179 11/10/2024 20:14:07