Write the composed trigonometric function sin(arctan x) in terms of x

∅ is an angle whose tangent function is

tan ∅=x/1

Considering the sides of the right triangle. 

We have 

opposite side =x,

adjacent side =1

and 

hypotenuse =√(x²+1)

Therefore 

the sine of this angle =opposite side/hypotenuse

sin ∅=x/√(x²+1)> the sign of sine ∅ will depend on the quadrant in which it is located

value of sin ∅ is positive>  ∅ belong to the first or second quadrant

value of sin ∅ is negative>  ∅ belong to the third or fourth quadrant

the answer is

x/√(x²+1)

1gm = 1000mg so 0.1gm = 1000mg

first, convert the weight to kg

160lb * 1kg/2.2lb = 72.7kg

next, the dose

72.7kg * 100mg/kg = 7270mg

the answer is y = 11.54

hope this : )