SUM OF 2 ANGLES (a + b)*
sin(a + b) = sin a cos b + cos a sin b
cos(a + b) = cos a cos b - sin a sin b
tg(a + b ) = tg a + tg b
1 - tg2a
DIFFERENCE OF 2 ANGLES (a - b)*
sin(a - b) = sin a cos b - cos a sin b
cos(a - b) = cos a cos b + sin a sin b
tg(a - b ) = tg a - tg b
1 + tg2a
DOUBLE ANGLES*
sin 2a = 2 sin a cos a
cos 2a = cos2a - sin2 a
= 2 cos2a - 1
= 1 - 2 sin2a
tg 2a = 2 tg 2a
1 - tg2a
sin a cos a = ½ sin 2a
cos2a = ½(1 + cos 2a)
sin2a = ½ (1 - cos 2a)
Commonly:
sin na = 2 sin ½na cos ½na
cos na = cos2 ½na - 1
= 2 cos2 ½na - 1
= 1 - 2 sin2 ½na
tg na = 2 tg ½na
1 - tg2 ½na
SUM OF DIFFERENCE BETWEEN 2 SAME ANGLE FUNCTIONS
MULTIPLY AND SUM FORM
sin a + sin b = 2 sin a + b cos a - b
2 2
sin a - sin b = 2 cos a + b sin a - b
2 2
cos a + cos b = 2 cos a + b cos a - b
2 2
cos a + cos b = - 2 sin a + b sin a - b
2 2
MULTIPLY ® SUM FORM*
2 sin a cos b = sin (a + b) + sin (a - b)
2 cos a sin b = sin (a + b) - sin (a - b)
2 cos a cos b = cos (a + b) + cos (a - b)
- 2 sin a cos b = cos (a + b) - sin (a - b)
SUM OF DIFFERENT FUNCTIONS
Bentuk a cos x + b sin x
Merubah bentuk a cos x + b sin x ke dalam bentuk K cos (x - a)
a cos x + b sin x = K cos (x-a)
K = Öa2 + b2 dan tg a = b/a Þ a = ... ?
Kuadran dari a ditentukan oleh kombinasi tanda a dan b sebagai berikut
I
|
II
|
III
|
IV
| |
a
|
+
|
-
|
-
|
+
|
b
|
+
|
+
|
-
|
-
|
keterangan :
a = koefisien cos x
b = koefisien sin x
a = koefisien cos x
b = koefisien sin x
EQUATION
I. sin x = sin a Þ x1 = a + n.360°
x2 = (180° - a) + n.360°
cos x = cos a Þ x = ± a + n.360°
tg x = tg a Þ x = a + n.180° (n = bilangan bulat)
a cos x + b sin x = C
K cos (x-a) = C
cos (x-a) = C/K
this equation can be solved by
-1 £ C/K £ 1 atau K² ³ C² (if K is in root form)
If C/K = cos b
cos (x - a) = cos b
(x - a) = ± b + n.360° ® x = (a ± b) + n.360°
This formulas are derived from this site. Spread credits to them first!
As for our test, I think the trigonometries would mostly contains of the topics ended by an asterisk (*).
Wish us luck in the test! (won't only wish you since I want to be lucky too huehuehue)
Bukannya itu semester 1 ya?
BalasHapusYupz. Tapi waktu wa kerja soal2x limit ama salah satu bab semester 2 (lali) masih sering ketemu rumus2x itu~
BalasHapus