SOLUTION: Evaluate the given expression without using a calculator. (Assume any variables represent positive numbers) Sin( arccos 3/5 + arctan 1/2)

Question 744764: Evaluate the given expression without using a calculator. (Assume any variables represent positive numbers)
Sin( arccos 3/5 + arctan 1/2)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Evaluate the given expression without using a calculator. (Assume any variables represent positive numbers)
Sin( arccos 3/5 + arctan 1/2)
***
let x=arccos 3/5
let y=arctan 1/2
..

..
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≈53.13�
tan(y)=1/2
y≈26.57�
x+y≈79.7�
sin(x+y)=sin79.7�≈0.9839
exact answer=(11√5)/25≈0.9839
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