Question

How do you find the exact functional value sin (-255 degrees) using the cosine sum or difference identity?

Answer 1

`sin(-255^@) = (1+sqrt(3))/(2sqrt(2))`

Explanation:

`sin(-255^@) = sin(105^@)`

`color(white)("XXXXXXX")=cos(90^@-105^@) = cos(-15^@)`

`color(white)("XXXXXXX")=cos(30^@-45^@)`

and by the cosine difference identity:
`color(white)("XXXXXXX")=cos(30^@) * cos(45^@)+sin(30^@) * sin(45^@)`

`color(white)("XXXXXXX")=sqrt(3)/2*1/sqrt(2)+1/2*1/sqrt(2)`

`color(white)("XXXXXXX")=(1+sqrt(3))/(2sqrt(2))`

and with the aid of a calculator:
`color(white)("XXXXXXX")~~0.965926` (but this is not "exact" as requested in question)