Answer
$cos 5^{ \circ}\approx 0.99619$
And the calculator gives: $0.996194696$
Work Step by Step
$cosx=\Sigma_{n=0}^{\infty}(-1)^{n}\frac{x^{2n}}{(2n)!}$
$5^{ \circ}\times \frac{\pi}{180}=0.087266463$
$1-\frac{0.087266463^{2}}{2!}\approx 0.99619$
Hence, $cos 5^{ \circ}\approx 0.99619$
and calculator gives $0.996194696$
