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

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Answer 1 · 2015-07-17T21:39:21

$sqrt2/2+1/2$

Recall the unit circle:

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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,

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