SOLUTION: If sin theta = -2/3 and tan > 0, find the exact value of the cosine and cotangent.

-2/3 is a negative number, so the sine is negative.
tanθ > 0 says the tangent is positive.

That tells us that θ is in QIII

So we draw the picture of θ.  We know that 


Since 

We draw a right triangle in QIII with opposite side -2
and hypotenuse +3.  We can use the Pythagorean theorem
to find the adjacent side or x,
adjacent = x = 
We take it negative because x, the adjacent side, goes to
the LEFT of the origin.



 

Since ,

. 

Since ,

.

Edwin