How do you find the exact functional value sin 405°+sin 120° using the cosine sum or difference identity?

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Answer 1 · 2015-08-27T21:59:55

#color(red)(sin(405) + sin(120) = (sqrt2+sqrt3)/2)#

#sin(405) = sin(360 + 45)#

The sine sum identity is:

#sin(A+B) = sinAcosB+cosAsinB#

∴ #sin(405) = sin(360)cos(45) + cos(360)sin(45)#

We can use the unit circle to work out the values.

#sin(405) = 0×sqrt2/2 + 1×sqrt2/2 = sqrt2/2#

#sin(405) + sin(120) = sqrt2/2 +sqrt3/2#

#sin(405) + sin(120) = (sqrt2+sqrt3)/2#