Question

Use differentials (or equivalently, a linear approximation) to approximate sin(27 degrees) as follows: Let f(x) = sin(x) and find the equation of the tangent line to f(x) at a nice point near 27 degrees. Then use this to approximate sin(27 degrees).

Answer 1

f(x) = sin(x)
df = cos(x) dx
So, since sin(30°) = 1/2

sin 27° = 1/2 + (√3/2)(-π/60)