Question

sin465°
$\sin(465)$
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Answer 1

$sin465^{\circ}=sin\left ( 105^{\circ}+360^{\circ} \right )=sin105^{\circ}=sin\left ( 45^{\circ}+60^{\circ} \right )\\sin45^{\circ}\cdot cos60^{\circ}+cos45^{\circ}\cdot sin60^{\circ}=\frac{\sqrt{2}}{2}\cdot \frac{1}{2}+\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2}=\frac{\sqrt{2}+\sqrt{6}}{4}$