trigonometry
TRANSCRIPT
1
RANGKUMAN RUMUS
3
Sin(a + b) = sin a . cos b + cos a . Sin b
Sin(a - b) = sin a . cos b – cos a . Sin b
Rumus jumlah dan selisih dua sudut
Cos(a + b) = cos a . cos b – sin a . Sin b
Cos(a - b) = cos a . cos b + sin a . Sin b
4
tan( + ) =
tan( - ) =
tan.tan1
tantan
tan.tan1
tantan
5
Rumus Sudut Rangkap
Sin 2a = 2 sin a . Cos a
Cos 2a = asinacos 22
asinacos 22
Cos 2a = 1acos2 2
Cos 2a = asin21 2
A
B
C tan 2a = atan1
atan22
Rumus Sudut Setengahan
sin a = 2
acos1A
B
C tan a =
2
1
cos a =2
12
acos1
2
1acos1
asin
asin
acos1
acos1
acos1
7
Rumus jumlah dan selisih sin dan cos
)ba(2
1sin).ba(
2
1sin2bsinasin
)ba(2
1sin).ba(
2
1cos2bsinasin
)ba(2
1cos).ba(
2
1cos2bcosacos
)ba(2
1sin).ba(
2
1sin2bcosacos
8
Rumus perkalian sin dan cos
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 . sin b = cos (a + b) – cos (a – b)
S + S
S – S
C + C
C - C
Menghafal Rumus
2 S C
2 C S
2 C C
– 2 S S
2
12
1
+ –
)ba(2
1cos).ba(
2
1sin2bsinasinSC2SS
)ba(sin)ba(sinbcos.asin2SSCS2
10
1. Sin 75o = …. Answer :
sin750 = sin(450 + 300)
= sin450cos300 + cos450sin300
= ½√2.½√3 + ½√2.½
= ¼√6 + ¼√2
= ¼√2(√3 + 1)
Example :Remember :
sin( + ) = sin.cos + cos.sin
11
2. Diketahui sin A = cos B =
A dan B adalah sudut-sudut lancip
sin(A – B) =….
Bahasan:
sin(A – B)= sin A cos B – cos A sin B
sin A =
cosA =
5
3
25
7
? ?
5
3
A
35
4 5
4 B
cos B =
sin B =
25
7
7
2524
25
24
12
sin(A – B) = sin A cos B – cos A sin B = x - x
=
=
5
325
7
5
4
25
24
125
96
125
21
5
3
125
75
13
Solve: cos cos + sin sin = cos ( - )
=
= =
....sinsincoscos 2813
75
2813
75
2813
75
2813
75 sinsincoscos )cos( 28
1375
)(cos 287
)(cos 4
22
1
14
1. tan 105° = …. Solve :
tan105° = tan(60° + 45°)
oo
oo
45tan.60tan1
45tan60tan
1.31
13
x31
31
31
31
15
tan 105° = x
=
=
=
= -2 - √3
31
31
31
31
31
)31( 2
31
3321
2
324
SELAMAT BELAJAR