Question

How do you use a linear approximation or differentials to estimate `tan44º`?

Answer 1

`~~ 0.965`

Explanation:

The derivative of `tan theta` is `sec^2 theta`, so that to a first order in `delta theta` we have

`tan(theta - delta theta) = tan(theta) -sec^2 theta xx delta theta`

To estimate `tan 44^circ` we must use `theta = pi/4` and `delta theta = pi/180` (remember that in calculus angles must be measured in radians) so that

`tan 44^circ ~~ tan (pi/4)-sec^2 (pi/4) xx pi/180 = 1-2 xx pi/180 ~~ 0.965`