Question 224142
What is the sin(ϴ) if x=6 and y=12
<pre><font size = 4 color = "indigo"><b>
Draw this

{{{ drawing(300,300,-4,9,-1,13, line(6,0,6,12),
 graph(300,300,-4,9,-1,13), line(0,0,6,0), line(6,12,0,0),
locate(3,1,"x=6"),locate(6.2,6,"y=12"), locate(2.1,7,"r=?"),
locate(1,1.5,theta)
   )}}}

Since sin(&#1012;){{{""= y/r}}}, we must find r by the
Pythagorean theorem:

{{{r^2=x^2+y^2}}}

{{{r^2=6^2+12^2}}}

{{{r^2=36+144}}}

{{{r^2=180}}}

{{{r=sqrt(180)}}}

{{{r=sqrt(36*5)}}}

{{{r=sqrt(36)sqrt(5)}}}

{{{r=6sqrt(5)}}}

So 

sin(&#1012;){{{""=y/r=12/(6sqrt(5))=2/sqrt(5)=2sqrt(5)/(sqrt(5)sqrt(5)) = 2sqrt(5)/5}}}