Use an appropriate local linear approximation to estimate the value of cotangent 44 degrees.

Answer 1

cotan 45 = 1

d cotan/dx = -csc^2 x
d cotan = -csc^2 x dx

here
csc^2 45 = (2/sqrt2)^2 = 4/2 = 2
dx = -1 deg * pi radians/180 deg = -.01745
and
y(x+dx) = y(x) + dy/dx * dx
so
cotan(44)= cotan (45) - 2(-.01745))
= 1 + .035
=1.035