How do you find the exact value of Sin 45degrees + cos 60degrees?

##sqrt2/2+1/2##
Recall the unit circle:
From the unit circle we can see that at ##45^o## the position of the angle on the unit circle is at ##(sqrt2/2sqrt2/2)##
##(sqrt2/2sqrt2/2)=(costhetasintheta)##
So for ##45^o## ##sin(45^o)=sqrt2/2##
Now from the unit circle we can see that at ##60^o## the position of the angle on the unit circle is at ##(1/2sqrt3/2)##
##(1/2sqrt3/2)=(costhetasintheta)##
So for ##60^o## ##cos(60^o)=1/2##
So
##sin(45^o)+cos(60^o)=sqrt2/2+1/2##