1) If  is an angle in quadrant 4 and , find the value of .

Since this involves drawing a graph in which  represents
the horizontal axis, not an angle,  I will temporarily change
 to  to avoid a conflict of letters.  Change
the problem to read this way:

1) If  is an angle in quadrant 4 and , find the value of .

We must use the identity:



However we do not know 

So we must first draw the picture of the angle :

We know that  is by definition , we
can draw the angle in the 4th quadrant with referent angle
is inside a triangle whose horizontal side  is taken
to be the numerator of , considered positive because
it goes right of the y-axis, and whose vertical side  is taken as 
the denominator , taken negative because it goes down
below the x-axis: 

 

Next we calculate  by the Pythagorean theorem:








So we label the slanted line segment . 

 

Now we can find 



So we substitute  for  in













±

Next we must decide whether this is positive or negative:

Since  is is the 4th quadrant, then 

° so multiplying that through by 

° 

The means  is in quadrant 2.  Since
the sine is positive in the 2nd quadrant, the final answer
is 

 

And of course now that we have the answer we can change
 back to :




2) What is the solution set of the equation

  =  in the interval ?

Use the identity  to replace  on the
left side:

  = 

  = 

 = 

 = 

 = 

Now use identity  to
replace 

 = 

Factor out 

 = 

Use the zero-factor principle:



3) Find the solution set of  over the domain °.



Use identity 




Multiply through by 







Use the zero-factor principle:
 


Edwin