How do you use differentials to estimate the value of #cos(63)#?
Approximating by differential = linear approximation = use the tangent line at a nearby point.
Answering This Question
I will assume that you want to approximate
At some point, either before we begin or within the functions we use, we'll have to change to radian measure. (Really we change to numbers.
(You could call the last 2 "radians", but I won't.)
I find the ideas more clear if we think about linear approximation, which is just approximating by a tangent line.
The linear (differential) approximation of
(This is the equation of the line tangent to the graph of the function at the point
We are approximating