Calc.
posted by Chelsea on .
Use a linear approximation (or differentials) to estimate the given number.
Tan 44 degrees
Please help.

f(x)=tan(x)
f'(x)=sec²(x)
Using linear approximation:
f(xo+δ)=f(xo)+δf'(xo) (approx.)
Put xo=π/4 (in radians, = 45°)
δ=π/180 (1°)
f(44°)
=f(xoδ)
=tan(π/4)δ*sec²(π/4) (approx.)
=1π/180/cos²(π/4)
=1π/180/(1/2)
=1π/90
=0.96509...
accurate value of tan(44°)=0.96569...