Answer
Local linear approximation: $cos(46^{\circ}) = -1$
Calculating device: $cos(46^{\circ}) = 0.96569 $
Thus, the local linear approximation produces a significantly different value.
Work Step by Step
$cot(46^{\circ}) = cot(45^{\circ} + 1^{\circ})$
In general, using the linear approximation: $cot(x + h) = cot(x) + cot'(x) * h$:
$cot(45^{\circ} + 1^{\circ})= cot(45^{\circ}) + cot'(45^{\circ}) * 1^{\circ}$
$cot(45^{\circ} + 1^{\circ}) = 1 + sec^2(45^{\circ}) * 1^{\circ}$
$cot(45^{\circ} + 1^{\circ}) = 1 -2 = -1$
Using a calculating device, we find $cos(46^{\circ}) = 0.96569 $
Thus, the local linear approximation produces a significantly different value.
