+118654 Isthere more to this question - like is this part c and you ahve already done the other bits or something?
+9665 The expression
= 2.5(10 cos 36 + 4 sin 35 - 3 cos 75)
= \(\dfrac{5(10\sin 54 + 4\sin 35 - 3\sin 15)}{2}\)
= \(\dfrac{5\left(10(\frac{1+\sqrt5}{4})+4((\sqrt[3]{-\frac{\sqrt6+\sqrt2}{32}+(\frac{i}{32})(2\sqrt{2-\sqrt3})})-\sqrt[3]{-\frac{\sqrt6+\sqrt2}{32}-(\frac{i}{32})(2\sqrt{2-\sqrt3})})-3(\dfrac{\sqrt3-1}{2\sqrt2})\right)}{2}\)
Upper part is
\(5\left(10(\frac{1+\sqrt5}{4})+4((\sqrt[3]{-\frac{\sqrt6+\sqrt2}{32}+(\frac{i}{32})(2\sqrt{2-\sqrt3})})-\\\sqrt[3]{-\frac{\sqrt6+\sqrt2}{32}-(\frac{i}{32})(2\sqrt{2-\sqrt3})})-3(\dfrac{\sqrt3-1}{2\sqrt2})\right)\)
I know this is complicated but it is completely real.
Source: http://intmstat.com/blog/2011/06/exact-values-sin-degrees.pdf
It has all exact values of sine of integers ranging from 1 - 90.
