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

Question

17930 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-17T21:39:21

#sqrt2/2+1/2#

Recall the unit circle:

enter image source here

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#