How do you find the exact functional value sin 195 using the cosine sum or difference identity?

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Answer 1 · 2015-08-27T20:41:14

#color(red)(sin(195) = (1-sqrt3)/(2sqrt2))#

I will use

#195 = 150 + 45#

∴ #sin(195)= sin(150+45)#

The sine sum identity is:

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

∴ #sin(195) = sin(150)cos(45) + cos(150)sin(45)#

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

#sin(195) = (1/2) sqrt 2/2+ (-sqrt3/2)sqrt2/2#

#sin(195) = sqrt2/4(1-sqrt 3)#

#sin(195) = (1-sqrt3)/(2sqrt2)#