Simplifier les formules Trigonométries de la Classe premier année secondaire on utilisant le power point

1. Done by Zein_el_dine Mayssoune

2. Trigonometric in grade 9
• in a right triangle ABC at A.
•
B
A C
𝛼 cos𝛼=
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑛𝑢𝑠𝑒
=
𝐴𝐵
𝐵𝐶
sin𝛼=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡ℎ𝑒𝑛𝑢𝑠𝑒
=
𝐴𝐶
𝐵𝐶
tan𝛼=
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
=
𝐴𝐶
𝐴𝐵
𝑠𝑖𝑛𝛼
𝑐𝑜𝑠𝛼

3. Trigonometric circle
(1;0)
(0;1)
(-1;0)
(0;-1)
(1;0) is the origin
of the trigonometric
circle

4. Orientation of a circle

5. Oriented angles
60°
- 60°
0
𝜋
2
𝜋
3𝜋
2

6. Principal determination
60° A
M𝐴𝑀 = 60° or
𝜋
3
𝐴𝑀 = 360°+ 60° or 2𝜋+
𝜋
3
𝐴𝑀 = 2 x 360° + 60°
Or 2(2𝜋) +
𝜋
3
𝐴𝑀 = 2K 𝜋+𝛼
𝛼 is the principal
determination of 𝐴𝑀
𝐴𝑀 =-360 + 60°
Or -2𝜋+60°

7. Trigonometric lines on the trigonometric circle
O Cos 𝛼
Sin𝛼
𝛼
Cos 𝛼 = 𝑥 𝑀
Sin 𝛼 = 𝑦 𝑀
Tan 𝛼 =
Sin 𝛼
Cos 𝛼
Cot 𝛼 =
1
Tan 𝛼
Tan𝛼
-1≤ Cos 𝛼 ≤ 1
-1≤ Sin 𝛼 ≤ 1

8. Signs of trigonometric lines
III
III IV
Quadrant I: 0 ≤ 𝛼 ≤
𝜋
2
cos 𝛼 ≥ 0 and 𝑆𝑖𝑛 𝛼 ≥ 0
Quadrant II:
𝜋
2
≤ 𝛼 ≤ 𝜋
cos 𝛼 ≤ 0 and 𝑆𝑖𝑛 𝛼 ≥ 0
Quadrant III: 𝜋 ≤ 𝛼 ≤
−𝜋
2
cos 𝛼 ≤ 0 and 𝑆𝑖𝑛 𝛼 ≤ 0
Quadrant IV:
−𝜋
2
≤ 𝛼 ≤ 0
cos 𝛼 ≥ 0 and 𝑆𝑖𝑛 𝛼 ≤ 0

9. Associated arc
𝛼
−𝛼
cos(-𝛼)=
sin(-𝛼)=
tan(-𝛼)=
cos(𝛼)
-sin(𝛼)
-tan(𝛼)

10. Associated arc
𝛼
𝜋 − 𝛼
cos(𝜋 -𝛼)=
sin(𝜋 -𝛼)=
tan(𝜋 -𝛼)=
- cos(𝛼)
sin(𝛼)
-tan(𝛼)

11. Associated arc
𝛼
𝜋 + 𝛼
cos(𝜋 + 𝛼)=
sin(𝜋 + 𝛼)=
tan(𝜋 + 𝛼)=
- cos(𝛼)
-sin(𝛼)
tan(𝛼)

12. Associated arc
cos(
𝜋
2
-𝛼)=
sin(
𝜋
2
-𝛼)=
tan(
𝜋
2
-𝛼)=
sin(𝛼)
cos(𝛼)
cot(𝛼) 𝛼
𝛼
𝜋
2
-𝛼

13. Associated arc
cos(
𝜋
2
+𝛼)=
sin(
𝜋
2
+𝛼)=
-sin(𝛼)
cos(𝛼)
𝛼
𝛼
𝜋
2
+𝛼
tan(
𝜋
2
+𝛼)=-cot(𝛼)