SOLUTION: sorry, these problems aren't from a textbook. I've started these four problems then just started going in circles to find the answer. 1.)Solve for x, where x is between 0 and 2pie

Write  for 



That doesn't factor, so we use the quadratic formula:



with , , and :







Using the +



Replace  by 



Use inverse tangent key on calculator,
with calculator in radian mode:



However, the calculator only gives the
answer which is in quadrant I.  There is
also another answer in quadrant III, because
the tangent is also positive in quadrant III.
To get that, we add :



Using the minus:





Use inverse tangent key on calculator,
with calculator in radian mode:



However, the calculator only gives the
negative answer which is in quadrant IV,
taken as a negative angle. However to get
a coterminal angle between 0 and ,
we add :


  
There is also another answer in quadrant II,
because the tangent is also negative in quadrant IV.
To get that, we add  to the




2.)verify the identity:




3.)evaluate:


Let's draw the picture of 

That means the angle whose sine is 

The inverse sine by definition is always between 
 and . Thus the angle  is in Quadrant I because 
is a positive number.

Since the sine =  we will let y be
the numerator of  and r be the
denominator.  

The angle  is



Now we need the cosine of this angle, which is , so
we will need the value of .  We use the Pythagorean theorem,









So now we have , so we put that in:



Therefore the cosine of that angle is  or 

So,




If I have time I'll come back to this:

4.) Given that sin theta =1/2, theta in Q1 and cos beta =1/2, find cos (theta-bata)


Edwin