Question

Let f(t)=sint where t is the measure of the angle in degrees. Thus f is the sin function on your calculator if you select degree mode. Then:

lim(t->0)(f(t)/t)=

(Your answer will be a real number.)

Answer 1

in radians

sin t --> t + t^2/2! -t^3/3!.....
so in radians
sin t/t --->1 as t--->0

however we are doing degrees
do t degrees which is (pi t/180) rad
so we have
sin (pi t/180) /t
which becomes
(pi t/180 +(pi t/180)^2/2 ...
divided by t
----> pi/180 as t--->0
----> .01745

check
sin .01 degrees / .01 = .01745 ..
whew !