1. Your observation is correct that Sin(6.8) on calculator = sin(radians(6.8) provided your calculator is set in degree units.
What you have used in Excel formulas [ sin(radians(6.8) ] is correct if; the angle 6.8 originally was in degrees. Was it in degrees? See the formulas you have attached in Excel. I do not think so. Why? Because circular frequency (w) is usually is rad/s. So your units are already in rad and you do not need convert them further and Excel is already set in rad units so just use directly the sin(6.8). This is what @Saad Pervez pointed out.