Page 16 - KELOMPOK 3_FLIPBOOK_PSPM 2020 A

PEMBAHASAN

Nomor Pembahasan Skor

1 a. sin 105 = sin(45° + 60°) = sin 45° 60° + 10
°
cos 45° sin 60°

1 1 1 1 1 1
= ( √ 2) ( ) + ( √ 2) ( √3) = √2 + √6
2 2 2 2 4 4
b. sin 165° = sin(135° + 30°) = sin 135° cos 30° + 10

cos 135° sin 30°
1 1 1 1 1 1
= ( √2) ( √3) + (− √2 ) ( ) = √6 − √2
2 2 2 2 4 4

2 sin 42° cos 18° + cos 42° sin 18° = sin(42° + 18° ) 10

1
= sin 60° = √3
2
3 a. cos 105° = cos(60° + 45°) = cos 60° cos 45° − 10

sin 60° sin 45°

1 1 1 1 1 1
= ( ) ( √2) − ( √3) ( √2) = √2 − √6
2 2 2 2 4 4
b. cos 195° = cos(150° + 45°) = cos 150° cos 45° −

sin 150° sin 45° `10
1 1 1 1 1 1
= (− √3) ( √2) − ( ) ( √2) = (− √6) − ( √2)
2 2 2 2 4 4

4 cos 195° cos 75° 10

+ sin 195° sin 195°
1
= cos(195° − 75°) = cos 120° = −
2
5 a. tan 105° = tan( 60° + 45°) = tan 60°+45° 10
1−tan60° tan 45°

√3 + 1 1 + √3 1 + √3 1 + 2√3 + 3
= = =
1 − (√3)(1) 1 − √3 1 + √3 1 − 3

4 + 2√3
= = −2 − √3
−2

Untuk Siswa SMA/MA Kelas XI 11