calculus
posted by Patricia on .
Use an appropriate local linear approximation to estimate the value of cotangent 44 degrees.

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