First, we need to express the angles in radians:
cos 3° = cos(3/180π) = cos(0.0524) ≈ 0.9986cos 27° = cos(27/180π) = cos(0.4712) ≈ 0.8849cos 60° = cos(60/180π) = cos(1.0472) = 0.5
sin 3° = sin(3/180π) = sin(0.0524) ≈ 0.9986sin 27°= sin(27/180π) = sin(0.4712) ≈ 0.8817sin 30° = sin(30/180π) = sin(0.5236) = 0.5
Next, we substitute these values into the expression:
0.9986 0.8849 0.5 - 0.9986 0.8817 0.5= 0.4424 - 0.4409= 0.0015
Therefore, the value of cos 3° cos 27° cos 60° - sin 3° sin 27° sin 30° is approximately 0.0015.
First, we need to express the angles in radians:
cos 3° = cos(3/180π) = cos(0.0524) ≈ 0.9986
cos 27° = cos(27/180π) = cos(0.4712) ≈ 0.8849
cos 60° = cos(60/180π) = cos(1.0472) = 0.5
sin 3° = sin(3/180π) = sin(0.0524) ≈ 0.9986
sin 27°= sin(27/180π) = sin(0.4712) ≈ 0.8817
sin 30° = sin(30/180π) = sin(0.5236) = 0.5
Next, we substitute these values into the expression:
0.9986 0.8849 0.5 - 0.9986 0.8817 0.5
= 0.4424 - 0.4409
= 0.0015
Therefore, the value of cos 3° cos 27° cos 60° - sin 3° sin 27° sin 30° is approximately 0.0015.