15 points! find the exact value of the composition. sin (arctan (2)) a) 2√5 / 5 b) 5√2 c) 2√5 d) 5√2 / 2

Focus on arctan 2 first.  This fact tells us that opp = 2 and adj = 1, so that the hyp is sqrt(4+1), or sqrt(5).

The sine of (arctan (2) ) is opp/hyp.  We know that opp=2 and hyp = sqrt(5).  
                                                           2sqrt(5)
Thus, sin (arctan (2)) = 2/sqrt(5)   or
                                                                 5