For mathematical exactitude, how do you express $sin 89.625^o$ , in a closed form?

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Answer 1 · 2016-11-12T04:22:26

$=sqrt(((1+sqrt(((1+sqrt((1+c(3))/2)))/2))/2)$ =0.999978581, nearly, where
$c(3)=cos(3^o)=(1/4)sqrt(8+sqrt3+sqrt15+sqrt(10-2sqrt5))$

Let $c(3) = cos (3^o)$ .

Now, s(89.625)#

$=c(90-89.625)$

$=c(0.375)$

$=sqrt((1+c(0.75)$

$=sqrt(((1+sqrt(((1+c(1.5)))/2)))/2)$

$=sqrt(((1+sqrt(((1+sqrt((1+c(3))/2)))/2))/2)$

For $c(3)=(1/4)sqrt(9-sqrt3+sqrt15+sqrt(10-2sqrt5))$ ,

For mathematical exactitude, how do you express sin 89.625^osin 89.625^o, in a closed form?