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anonymous
 5 years ago
Without using a calculator determine the exact value of sin(x  y) given that cos x = (1/3) , tan y = (1/3) , x is a quadrant III angle and y is a quadrant III angle.
anonymous
 5 years ago
Without using a calculator determine the exact value of sin(x  y) given that cos x = (1/3) , tan y = (1/3) , x is a quadrant III angle and y is a quadrant III angle.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sin(xy) = sin(x) cos(y)  sin(y) cos(x) \[=(2\sqrt{2})(3\sqrt{10})  (\sqrt{10})(1/3)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Possible answers are \[A. (12\sqrt{5}  \sqrt{10})/ 30 B. (12\sqrt{5} + \sqrt{10})/ 30 C. 42 D. (12\sqrt{5} + \sqrt{10})/ 3 E. (12\sqrt{5}  \sqrt{10})/ 300\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How do I multiply those all together? Im never good with radicals

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0see the attachment for clearer explanation. (−2√2)(−3√10)−(−√10)(−1/3)= (6√20)  ( 1/(3√10) ) √20 = √4 √5 = 2√5 therefore 6√20 = 12√5 ( 1/(3√10) ) = √10/30 so > (6√20)  ( 1/(3√10) ) = (12√5)  (√10/30)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, i think i plug the wrong values

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let's do this from the beginning sin(xy) = sin(x) cos(y)  sin(y) cos(x)\[(2\sqrt{2}/3)(3/\sqrt{10})  (1/\sqrt{10})(1/3)\]\[=(6\sqrt{2}/3\sqrt{10})  (1/3\sqrt{10})\]\[=6\sqrt{2}1\over3\sqrt{10}\] \[=6\sqrt{20}\sqrt{10}\over 30\] \[=12\sqrt{5}\sqrt{10}\over30\]
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