Question

Sa se calculeze: A)sin 75; B)cos 75; C)sin 405

Answer 1

$a)\sin 75=\sin(30\textdegree+45\textdegree)=\sin30\textdegree\cdot \cos 45\textdegree+\sin45\textdegree\cdot \cos 30\textdegree= \\ =\dfrac{1}{2}\cdot \dfrac{\sqrt2}{2}+\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt 3}{2}=\boxed{\dfrac{\sqrt 6+\sqrt 2}{4}}\\ b)\cos75\textdegree =\cos(30\textdegree +45\textdegree)=\cos 30\textdegree \cdot \cos 45 \textdegree -\sin 30 \textdegree\cdot \sin 45\textdegree= \\ =\dfrac{\sqrt 3}{2}\cdot \dfrac{\sqrt 2}{2}-\dfrac{1}{2}\cdot \dfrac{\sqrt 2}{2}=\boxed{\dfrac{\sqrt 6-\sqrt 2}{4}}$

$c)\sin 405\textdegree=\sin(360\textdegree+45\textdegree)=\sin 45\textdegree= \dfrac{\sqrt2}{2}$