To simplify the expression, we first need to convert all angles to their equivalent in the first quadrant.
sin(690°) = sin(690° - 360°) = sin(330°) = -sin(30°) = -0.5cos(210°) = cos(210° - 180°) = cos(30°) = 0.866ctg(660°) = ctg(660° - 360°) = ctg(300°) = ctg(60°) = 1/√3
Now we substitute these values back into the expression:4(-0.5) - 8(0.866) + (1/√3)= -2 - 6.928 + 0.577= -9.351
Therefore, the simplified value is -9.351.
To simplify the expression, we first need to convert all angles to their equivalent in the first quadrant.
sin(690°) = sin(690° - 360°) = sin(330°) = -sin(30°) = -0.5
cos(210°) = cos(210° - 180°) = cos(30°) = 0.866
ctg(660°) = ctg(660° - 360°) = ctg(300°) = ctg(60°) = 1/√3
Now we substitute these values back into the expression:
4(-0.5) - 8(0.866) + (1/√3)
= -2 - 6.928 + 0.577
= -9.351
Therefore, the simplified value is -9.351.