Find approximate value #tan(44^circ)#?

1 Answer
Feb 20, 2018

#"Approx., "1-pi/90#.

Explanation:

We know that, #f(x+deltax)~~f(x)+f'(x)deltax#.

Let, #f(x)=tanx (x" in radian), so that, "f'(x)=sec^2x#.

Letting #x=45^@=pi/4 and deltax=-1^@=-pi/180#, we have,

#f(45^@-1^@)=f(pi/4-pi/180)~~f(pi/4)+f'(pi/4)(-pi/180)#.

Equivalently,

#tan44^@=tan(pi/4-pi/180)~~tan(pi/4)-pi/180sec^2(pi/4)#.

#rArr tan44^@~~1-pi/90#.