Doubled angle formulas trigonometry .ppt

Trigonometry formulas on doubled angles

1. IKKILANGAN IKKILANGAN
BURCHAK BURCHAK
FORMULALARIFORMULALARI

2. QO’SHISH
FORMULALARI
sin
)cos(
tg
 sincoscossin 
 sinsincoscos 


tgtg
tgtg


1

3.   cossin2sincoscossinsin 

22
sincossinsincoscos)cos( 






2
1
2
1 tg
tg
tgtg
tgtg
tg







4. IKKILANGAN BURCHAK
FORMULALARI

5. 1-misol

6. Yechim:
 cossin22sin
 
22
cos1sin  36,064,018,01
2

6,036,0sin 
-0,6sin 
 8,06,022sina 96,0

7. 2-misol. Soddalashtiring
.
50cos
100sin
0
0

0
0
50cos
100sin


0
0
50cos
502sin

0
00
50cos
50cos50sin2
.50sin2
0

8. 3-misol. Soddalashtiring
.
6cos
3cos3sin
a
aa


a
aa
6cos
3cos3sin


a
aa
6cos
3cos3sin2
2
1


a
aa
6cos
)3cos3sin2(
2
1


a
a
6cos
32sin
2
1


a
a
6cos
6sin
2
1
.6
2
1
atg

9. 4-misol. Soddalashtiring
.2coscos
2

 2coscos
2
  aa
222
sincoscos
 aa
222
sincoscos .sin
2
a

10. Soddalashtiring
2
22
00
22
0202
00
8
sin
8
cos.5
15cos15sin.4
8
sin
8
cos.3
75sin75cos.2
75cos75sin2.1










