Answer
$cos~29^{\circ} \approx 0.87475$
Work Step by Step
Let $y = cos~x$
$\frac{dy}{dx} = -sin~x$
$dy = (-sin~x)~dx$
We can express $29^{\circ}$ in units of radians:
$29^{\circ} = (\frac{\pi}{6}-\frac{\pi}{180})~rad$
Let $x = \frac{\pi}{6}$ and let $dx = -\frac{\pi}{180}$
$dy = (-sin~\frac{\pi}{6})~(-\frac{\pi}{180})$
$dy = (\frac{1}{2})~(\frac{\pi}{180})$
$dy = \frac{\pi}{360}$
We can find an approximation for $cos~29^{\circ} = cos~(\frac{\pi}{6}-\frac{\pi}{180})$
$cos~29^{\circ} \approx cos(\frac{\pi}{6}) +\frac{\pi}{360}$
$cos~29^{\circ} \approx \frac{\sqrt{3}}{2}+\frac{\pi}{360}$
$cos~29^{\circ} \approx 0.87475$
