The main trigonometrically ratios of the acute angle
1] Lesson objectives:
After the end of this lesson the student should be able to:
-
Get the main trigonometrically ratios of the acute angle
Deal with the mathematical activities in groups
Communicate mathematically orally and written
Build mathematical connections among mathematical knowledge and life situations
2] Learning tools and resources:
Text book - Hand out & worksheets – calculator – Markers
3] Previous experience:
[15 minutes]
?2 = 42 + 32 = 25
? = √25 = 5 𝑐𝑚
?2 = 132 − 52 = 144
? = √144 = 12 cm
?
5cm
?
4cm
13cm
3cm
Complete:
2
2
1) 34.6° = ⋯ ° …\ …\\
2) 78.08° = ⋯ ° …\ …\\
3) 76° 16\ =
...°
4) 85° 38\ 8\\ = … … … … °
2
? = 25 − 20 = 225
? = √225 = 15 cm
20cm
Remember that:
1) If a and b are two complementary
angles
Than a + b = 90°
2) If a and b are two supplementary
angles
Than a + b = 180°
?
25cm
4] Lesson activities:
[15 minutes]
- Opening the idea
X
H
Hypotenuse
O
Opposite to ∠ Z
A
H
Hypotenuse
O
Opposite to ∠ X
X
H
O
Adjacent to ∠ Z
Z
H
A
A
Y
Adjacent to ∠ X
H
Z
1
A
O
Y
A
Complete:
1)
2)
3)
4)
5)
The hypotenuse of triangle ABC is . . . . . .
The adjacent side to angle C is . . . . . .
The opposite side to angle C is . . . . . .
The adjacent side to angle A is . . . . . .
The opposite side to angle A is . . . . . .
𝑂
Sin C =
𝐻
𝐴
Cos C =
=
B
A
C
AB
AC
CB
=
𝐻 AC
𝑂 AB
Tan C = =
𝐴 BC
B
C
A
M
?
10
O
Sin N =

B
N
26
Complete:Sin O =
17
Cos O =
Complete:Sin A =
Cos A =
Tan A =
Sin C =
Tan C =
Tan O =
Cos N =
Cos C =
Tan N =
Developing the idea:
Ex:
1)
2)
3)
4)
[30 minutes]
X
Complete:XZ =
Sin X =
Cos X =
Tan X =
Sin Z =
Cos Z =
Tan Z =
4
Prove that Sin X Cos Z + Cos X Sin Z = 1
Z
Find 1 + Tan2 Y

C
8
In opposite figure Find
3
Y
A
34 Cos B+32 Tan B
Sin2 A+Cos2 A
Solution
17cm
(AC)2 = (AB)2 – (CB)2 =172- 82 = 225
AC = √225 = 15 cm
8
17
Cos B =
, Tan B =
15
8
8
17
, Sin A =
Cos A =
15
17
B
2
8cm
C
34 Cos B + 32 Tan B = 34 ×
8 2
8
15
+ 32 ×
= 16 + 60 = 76
17
8
15 2
Sin2 A + Cos2 A = (17) + (17) = 1
∴
34 Cos B + 32 Tan B
= 76 ÷ 1 = 76
Sin2 A + Cos 2 A
Drill
Closing the idea:
Performance assessment:
Enhancement activities:
Student\ s portfolio
Page 55 no. 8,9,10
3
The main trigonometrically ratios of some angles
1] Lesson objectives:
After the end of this lesson the student should be able to:
- Get the main trigonometrically ratios of some angles
- Deal with the mathematical activities in groups
- Communicate mathematically orally and written
- Build mathematical connections among mathematical knowledge and life situations
2] Learning tools and resources:
Text book - Hand out & worksheets – calculator – Markers
3] Previous experience:
[15 minutes]
Drill
Complete
Sin 30 = Cos ………,
Cos 30 = sin ……...,
Tan 60 = tan ……..
4
4] Lesson activities:
- Opening the idea
[15 minutes]
5
-
Developing the idea:
 Find m ∠ X if
1) Sin X = 0.4
2) Cos X = 0.741
3) Tan X = 20345
4) Sin 2X = 0.5
[30 minutes]
5) Sin X = Sin 30 Cos 60 + Cos 30 Sin 60
6) Cos X – 1 = zero
7) Tan (X + 20) = √𝟑
6
Closing the idea:
Performance assessment:
 Find m ∠A and m ∠ C in each of the following:A
A
9
5
C
B
3
Enhancement activities:
 In opposite figure
A
C
7
B
6
A
Find 1) m ∠B
2) Area of triangle ABC
C
2
5
Student\ s portfolio
Page 61 no. 1,2,3,4
B
C
7
3
D
B
Unit test
1] Lesson objectives:
After the end of this lesson the student should be able to:
- Get the main trigonometrically ratios of some angles
- Deal with the mathematical activities in groups
- Communicate mathematically orally and written
- Build mathematical connections among mathematical knowledge and life situations
2] Learning tools and resources:
Text book - Hand out & worksheets – calculator – Markers
3] Previous experience:
[15 minutes]
8
4] Lesson activities:
- Opening the idea
-
[15 minutes]
Developing the idea:
[30 minutes]
9
Closing the idea:
Performance assessment:
Enhancement activities:
10
Distance between two points
1] Lesson objectives:
After the end of this lesson the student should be able to:
- Get the distance between two points
- Deal with the mathematical activities in groups
- Communicate mathematically orally and written
- Build mathematical connections among mathematical knowledge and life situations
2] Learning tools and resources:
Text book - Hand out & worksheets – calculator – Markers
3] Previous experience:
[15 minutes]
4] Lesson activities:
- Opening the idea
[15 minutes]
11
-
Developing the idea:
[30 minutes]
12
Closing the idea:
Performance assessment:
Student\ s portfolio
Page 67 no second
13
Exercises on Distance between two points
1] Lesson objectives:
After the end of this lesson the student should be able to:
- Solve exercises distance between two points
- Deal with the mathematical activities in groups
- Communicate mathematically orally and written
- Build mathematical connections among mathematical knowledge and life situations
2] Learning tools and resources:
Text book - Hand out & worksheets – calculator – Markers
3] Previous experience:
[15 minutes]
14
15
16
17
18
19