1.simplify with the aid of a calculator
Keys: " =degrees
sin21"40^1+cos23"50^1
by 21"40^1, I will assume you mean
21° 40 minutes and 1 second
1 second = 1/3600 of a degree
1 minute = 1/60 of a degree
so 21"40^1
= 21 + 40/60 + 1/3600
= 21.66694444..
so sin(21.6669444..) = .3692106...
do the same for the second term, then add them up
On most scientific calculators, you will find a key
labeled D°M'S
so enter
21
press D°M'S
40
press D°M'S
1
press D°M'S
press =
press sin
press = , to get .369210... as above