SOLUTION: P(11,-4) is a point on the terminal arm of the angle θ in standard position. Calculate sin θ and give your answer to 3 decimal places.

We plot the point P(11,-4), draw a line from it to the origin,
so as to make a right triangle with the side opposite θ as the
y coordinate of P, and the adjacent side as the x-coordinate
of P.  The red arc is the angle θ, and the reference angle
is the one inside the right triangle next to the x-axis. We
use the reference angle to determine the adjacent and opposite
sides. 



The sine is the opposite side over the hypotenuse.
The opposite side of θ is the y-ccoordinate of the
point P which is -4.  The adjacent side of θ is the
x-coordinate of P which is 11.  

We need to calculate the hypotenuse by the Pythagorean
theorem







So we put  on the hypotenuse:

   

Now , so



So if we round to 3 decimal places, the answer is

 <--the negative sign is very important!

Edwin