TRIGONOMETRIVIII . 2 sin A cos B , 2 cos A sin B

Kelompok VIII

Kelas XI – IPA 1

• ALIEN NURIL WARDANI (03)• IQBAL SYARIFULLAH (18)• NURIYA FADILAH (28)• SEPTIN DWI AULIA N (33)

Asal Rumus 2 sin A cos B

sin ( A + B ) = sin A cos B + cos A sin B

sin ( A – B ) = sin A cos B – cos A sin B +

sin ( A + B) + sin ( A – B ) = 2 sin A cos B

RUMUS :sin ( A + B) + sin ( A – B ) = 2 sin A cos B

Asal Rumus 2 cos A sin B

sin ( A + B ) = sin A cos B + cos A sin B

sin ( A – B ) = sin A cos B – cos A sin B -

sin ( A + B) - sin ( A – B ) = 2 cos A sin B

RUMUS :sin ( A + B) - sin ( A – B ) = 2 cos A sin B

Contoh Soal

1. 2 sin 60 cos 30 = ...........

Jawab :

sin ( 60 + 30 ) + sin ( 60 – 30 ) =

sin 90 + sin 30 =

1 + ½ =

1.5

Contoh Soal

2. Sin A cos B = ...............

Jawab :

Latihan Soal

1. 2 sin 52,5 cos 7,5 = ............

2. 6 sin 105 cos 15 = ............

3. 5 cos 37,5 sin 7,5 = ............

Penyelesaian

1. 2 sin 52,5 cos 7,5 =

Jawab :

sin ( 52,5 + 7,5 ) + sin ( 52,5 – 7,5 ) =

sin 60 + sin 45 =

½ √3 + ½ √2

Penyelesaian

2. 6 sin 105 cos 15 =

=

= 3 ( sin 120 + sin 90 )

= 3 ( ½ √3 + 1 )

= 3/2 √3 + 3

Penyelesaian

3. 5 cos 37,5 sin 7,5 =

=

= ( cos 45 – sin 30 )

= ( ½ √2 + ½ √3 )

= 5/4 √2 + 5/4 √3

TERIMA KASIH

Atas Perhatian Teman – teman dan Bapak Heru

WASSALAMUALAIKUM Wr, Wb.