Question 1104079
An acute angle θ is in a right triangle with
 sin θ = 3/4. What is the value of cot θ?
<pre>
Since the sine equals opposite over hypotenuse, draw a right 
triangle with angle &#952; having its opposite side equal to 
the numerator of 3/4, which is 3, and hypotenuse equal
to the denominator of 3/4, which is 4.

{{{drawing(200,180,-1,3.5,-1,4, 
locate(.4,.45,theta),locate(2.75,1.5,3),locate(1,1.7,4),
triangle(0,0,sqrt(7),0,sqrt(7),3)  )}}}{{{matrix(13,1,
Then, we, calculate, the, adjacent, side, using, the,
Pythagorean,theorem, sqrt(4^2-3^2)="",sqrt(16-9)="",sqrt(7))}}}{{{drawing(200,180,-1,3.5,-1,4, 
locate(.4,.45,theta),locate(2.75,1.5,3),locate(1,1.7,4),
triangle(0,0,sqrt(7),0,sqrt(7),3),locate(1.3,0,sqrt(7))  )}}}{{{matrix(5,1,
Since,cot(theta)=adjacent/(opposite),we,have,cot(theta)=sqrt(7)/3)}}}

Edwin</pre>