SOLUTION: Find the exact value of {{{sin(2theta)}}} if {{{cos(theta) = -sqrt(5)/3}}} and {{{"180°"<theta<"270°"}}}

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Question 349081: Find the exact value of if and
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Find the exact value of if and
We draw the approximate graph of the angle  in quadrant III,
since it is between 180° and 270°.



Since , and since ,
we take , the numerator of the cosine and ,
the denominator of the cosine, draw a perpendicular from the terminal
side of  to the x-axis, and label the horizontal side
of the resulting triangle , (negative because it goes
to the left), and the hypotenuse .  The hypotenuse  is 
always taken positive:



Now we use the Pythagorean theorem to find the length of
the vertical side:






 

Since the vertical side of the right triangle goes
down from the x-axis, we label it negative as 



Next we want to find .

We use the identity:



We substitute and 





Edwin

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