Question

Find the exact value of sin(255∘)

Answer 1

Check the picture below.

`\textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(255^o)\implies sin(135^o+120^o) \\\\\\ sin(135^o)cos(120^o)~~ + ~~cos(135^o)sin(120^o) \\\\\\ \left( \cfrac{√(2)}{2} \right)\left( -\cfrac{1}{2} \right)~~ + ~~\left( -\cfrac{√(2)}{2} \right)\left( \cfrac{√(3)}{2} \right)\implies -\cfrac{√(2)}{4}~~ - ~~\cfrac{√(6)}{4}\implies \cfrac{-2-√(6)}{4}`