(Solved): 59. Find the even and odd parts of each of these functions. (a) \( \mathrm{g}(t)=10 \sin (20 \pi t ...

59. Find the even and odd parts of each of these functions. (a) \( \mathrm{g}(t)=10 \sin (20 \pi t) \) (b) \( \mathrm{g}(t)=20 t^{3} \) (c) \( \mathrm{x}(t)=8+7 t^{2} \) (d) \( \mathrm{x}(t)=1+t \) (e) \( \mathrm{x}(t)=6 t \) (f) \( \mathrm{g}(t)=4 t \cos (10 \pi t) \) (g) \( \mathrm{g}(t)=\frac{\cos (\pi t)}{\pi t} \) (h) \( \mathrm{g}(t)=12+\frac{\sin (4 \pi t)}{4 \pi t} \) (i) \( \mathrm{g}(t)=(8+7 t) \cos (32 \pi t) \) (j) \( \mathrm{g}(t)=\left(8+7 t^{2}\right) \sin (32 \pi t) \)