How do you find the exact functional value sin 11/12 pi using the cosine sum or difference identity?

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Answer 1 · 2015-08-27T20:14:52

#color(red)(sin((11π)/12) = (sqrt3-1)/(2sqrt2))#

There are several different ways to answer this question.

I will arbitrarily use

#(11π)/12 = (8π)/12 + (3π)/12 = (2π)/3+π/4#

∴ #sin((11π)/12)= sin((2π)/3+π/4)#

The sine sum identity is:

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

∴ #sin((11π)/12) = sin((2π)/3)cos(π/4) + cos((2π)/3)sin(π/4)#

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

#sin((11π)/12) = sqrt3/2× sqrt2/2 + (-1/2) sqrt 2/2#

#sin((11π)/12) = sqrt2/4(sqrt 3-1)#

#sin((11π)/12) = (sqrt3-1)/(2sqrt2)#