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Buddhist Yip Kei Nam Memorial College
Secondary Four
Mathematics worksheet 2
Name： _____________________
Class (class no.)： _______ (
Trigonometric Ratios of Some Special Angles
1.
P.1
)
30 及 60
In the figure, ABC is a equilateral triangle with length
of side is 2,
Find the length of AD
2.
45
In the figure, ABC is a right – angled isosceles triangle
with AB = BC = 1
Find the length of AC
Using the relationships between the angles and sides of the right – angled isosceles triangle and
equilateral triangle, find out the trigonometric ratios of some special angles.
( Express your answer in surd form)
Trigonometric
Ratio
30
60
45
sin 
cos 
tan 
Trigonometric Identities
1. Refer to the figure, write down the following trigonometric ratio
(a) tan  =
sin  =
cos  =
sin 
=
cos 
Conclusion ： [
]
(b) (sin )2 + (cos )2 =
Conclusion ： [
]
Corollary 1.
Corollary 2
] and
]
[
[
P.2
Simplify
3 sin 
1.
cos 
3. 5 sin2  + 5 cos2 
2. cos  tan  + sin 
4. 2 – 2 sin2 
6. 1 + tan 2 
4  4 cos 2  .
tan  cos 2 
7  7 sin 2 
7.
8.
cos 
sin 
Trigonometric Ratio of the complementary angle ( 90 –  )
Refer to the figure, write down the following trigonometric ratio
5.
2.
sin  =
cos  =
tan  =
sin ( 90 –  ) =
cos ( 90 –  ) =
tan ( 90 –  ) =
sin ( 90 –  ) =
cos ( 90 –  ) =
tan ( 90 –  ) =
Conclusion ： [
]
(a) Refer the above result and using the calculator to complete the following table.
( answers should be corrected to 3 decimal places if necessary.)

60
30
45
38
76
sin ( 90 –  )
cos 
cos ( 90 –  )
sin 
tan ( 90 –  )
1
tan 
(b) Complete the following table
(i) sin 20 = cos (
(iv) cos 81 = sin (
(vii)
1
=
tan 57
tan (
)
(ii) cos 15 = sin (
)
(v) tan 64 =
)
(iii) tan 40 =
)
1
tan (
(viii) sin 73 = cos (
1
tan (
)
(vi) sin 59 = cos (
)
(ix) cos 32 = sin (
)
)
)
Exercise 1
Find the value in each of the following questions.
3
1. sin 60 + cos 30
2.
tan 60
4.
tan 60
tan 30
8.
Exercise 2
Simplify the following questions
tan 
1.
2.
sin 
2
1

cos 30 sin 60
tan 2
1  tan 2
4. (1 – sin )(1 + sin )
7.
4 sin 
sin (90   )
8.
1
tan 80
cos (90   )
3 sin 
tan 2
1  cos 2
sin  cos  (1 + tan 2 )
tan 27 tan 63
5. tan 10 –
9. cos 30 + tan 45 sin 60
3.
5.
Exercise 3
Simplify the following questions.
1. sin 25 – cos 65
2.
sin 43
cos 47
6. cos 60 – 2 cos 30
5. sin2 60
7. (2 sin 30 tan 30)2
4.
3. sin 45 cos 60
3. cos 2 21 + cos 2 69
6. cos 35 sin 55 + cos 55 sin 35
9.
sin 
 tan (90   )
cos 