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))#,