Question 744764
Evaluate the given expression without using a calculator. (Assume any variables represent positive numbers) 
Sin( arccos 3/5 + arctan 1/2)
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let x=arccos 3/5
let y=arctan 1/2
..
{{{cos(x)=3/5}}}
{{{sin(x)=sqrt(1-cos^2(x))=sqrt(1-9/25)=sqrt(16/25)=4/5}}}
..
{{{tan(y)=1/2=sin(y)/cos(y)}}}
{{{sin(y)=1/sqrt(5)}}}
{{{cos(y)=2/sqrt(5)}}}
..
Sin( arccos 3/5 + arctan 1/2)=sin(x+y)
=sin(x) cos(y)+cos(x) sin(y)
=4/5*2/√5+3/5*1/√5
=8/5√5+3/5√5=11/(5√5)
=(11√5)/25
..
Check: (with calculator)
cos(x)=3/5
x≈53.13º
tan(y)=1/2
y≈26.57º
x+y≈79.7º
sin(x+y)=sin79.7º≈0.9839
exact answer=(11√5)/25≈0.9839