Question

how do i find the exact value of sin(arctan(2))? I think it's in first quadrant but how do i start this problem?

Answer 1

\[\text{ Let} \theta=\arctan(2) => \tan(\theta)=2=\frac{2}{1}=\frac{opp}{adj}\]

Answer 2

the hyp is \[\sqrt{2^2+1^2}=\sqrt{5}\]

Answer 3

\[\sin(\arctan(2))=\sin(\theta)=\frac{opp}{hyp}=\frac{2}{\sqrt{5}}\]

Answer 4

Excellent step by step explanation. Thank you!