SOLUTION: sqrt(9-x^2) where x=3sin...i understand it is factoring and i know the answer is 3|cos| i just am having problems so i see the question to this point sqrt(9-3sin^2)

Algebra ->  Trigonometry-basics -> SOLUTION: sqrt(9-x^2) where x=3sin...i understand it is factoring and i know the answer is 3|cos| i just am having problems so i see the question to this point sqrt(9-3sin^2)      Log On


   



Question 567036: sqrt(9-x^2) where x=3sin...i understand it is factoring and i know the answer is 3|cos| i just am having problems so i see the question to this point
sqrt(9-3sin^2)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%289-x%5E2%29

sqrt%289-%283sin%28x%29%29%5E2%29  <-- notice that the 3 must be inside parentheses
                as a coefficient of sin(x). That was an
                error you made.  That is, the 3 is squared
                along with the sin(x).  The way you had it
                the 3 was not squared as it should have been.  

sqrt%289-3%5E2sin%5E2%28x%29%29

sqrt%289-9sin%5E2%28x%29%29

sqrt%289%281-sin%5E2%28x%29%29%29

sqrt%289%29sqrt%281-sin%5E2%28x%29%29

3sqrt%281-sin%5E2%28x%29%29

3sqrt%28cos%5E2%28x%29%29

Since the cosine is sometimes negative, but
the square root of its square when written with a
radical is never negative.  Therefore we must
put absolute value bars around the square root to
prevent it from ever being negative:

Answer 3abs%28cos%28x%29%29

Edwin