Question

Va rogggggg!!!!Calcule ușoare!!!​

Answer 1

FORMULE:

sin ( a + b ) = sin a • cos b + sin b • cos a

sin ( a - b ) = sin a • cos b - sin b • cos a

cos ( a + b ) = cos a • cos b - sin a • sin b

cos ( a - b ) = cos a • cos b + sin a • sin b

REZOLVARE:

• sin 15° = sin ( 45° - 30° ) =

= sin 45° • cos 30° - sin 30° • cos 45° =

= ✓2/2 • ✓3/2 - 1/2 • ✓2/2 =

= ✓6/4 - ✓2/4 = ( ✓6 - ✓2) / 4

• sin 75° = sin ( 45° + 30° ) =

= sin 45° • cos 30° + sin 30° • cos 45° =

= ✓2/2 • ✓3/2 + 1/2 • ✓2/2 =

= ✓6/4 + ✓2/4 = (✓6 + ✓2 ) / 4

• sin 135° = sin ( 75° + 60° ) =

= sin 75^ • cos 60° + sin 60° • cos 75°

Pentru asta avem nevoie sa calculăm cos 75°

cos 75° = cos ( 45° + 30° ) =

= cos 45° • cos 30° - sin 45° • sin 30° =

= ✓2/2 • ✓3/2 - ✓2/2 • 1/2 =

= ✓6/4 - ✓2/4 = (✓6 - ✓2) / 4

revenim la exercițiu

= ✓6 + ✓2 /4 • 1/2 + ✓3/2 • ✓6 - ✓2 /4 =

= (✓6 + ✓2 ) / 8 + (✓18 - ✓ 6) / 8 =

= ( ✓6 + ✓ 2 + 3 ✓ 2 - ✓ 6 / 8 =

= 4✓2/8 = ✓2/2

• sin 120° = sin ( 60° + 60° )=

= sin 60° • cos 60° + sin 60° • cos 60° =

= ✓3/2 • 1/2 + ✓3/2 • 1/2 =

= ✓3/4 + ✓3/4 = 2✓3/4 = ✓3/2

• sin 150° = sin ( 75° + 75° )=

= sin 75° • cos 75° + sin 75° • cos 75° =

= (✓6 + ✓2) / 4 • (✓6 - ✓2) / 4 + (✓6 + ✓2)/4 • (✓6 - ✓2) /4 =

= 2 • (✓6+✓2)(✓6-✓2)/16 =

= ✓6² - ✓2² / 8 = 6-2 /8 = 4/8 = 1/2

1) a) sin 17° • cos 13° + cos 17° • sin 13° =

= sin ( 17° + 13° ) = sin 30° = 1/2

b) cos 73° • cos 17° - sin 73° • sin 17° =

= cos ( 73° + 17° ) = cos 90° = 0

2) sin 60° - cos 30° = ✓3/2 - ✓3/2 = 0