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 ##(sqrt2/2,sqrt2/2)##

##(sqrt2/2,sqrt2/2)=(costheta,sintheta)##

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 ##(1/2,sqrt3/2)##

##(1/2,sqrt3/2)=(costheta,sintheta)##

So, for ##60^o##, ##cos(60^o)=1/2##

So,

##sin(45^o)+cos(60^o)=sqrt2/2+1/2##