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anonymous
 5 years ago
Without using a calculator determine the exact value of sin(x  y) given that sin x = 1/3) , tan y = (1/3) , x is a quadrant II 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 sin x = 1/3) , tan y = (1/3) , x is a quadrant II 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(x) shouldn't be negative if x is in the second quadrant. Is there a typo?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Im sorry the problem is Without using a calculator determine the exact value of cos(x  y) given that sin x = (1/3) , tan y = (1/3) , x is a quadrant II angle and y is a quadrant III angle.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0use sum/diff of angle expansion

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0= cos(x)cos(y)+sin(x)sin(y)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if sin(x) = (1/3) , draw up a general right angle triangle , mark an angle x ( obviously not the right angle ) , and label the opposite 1 and hypotenuse 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then you can find the adjacent side by pythagorus , which works out as sqrt(8) therefore cos(x) =  sqrt(8) / 3 ( because x is negative in the 2nd quadrant

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now you just need to find siny and cosy

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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0with tan(y)=(1/3) , draw up a general right angle triangle , mark opposite as 1 and adjacent as 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0therefore the hypotenuse is sqrt(10) so sin(y) =  1 / sqrt(10) and cosy = 3/sqrt(10)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So my equation should look like (sqrt(8)/3 * 3/sqrt(10) ) + (1/3 * 1/sqrt(10)) ???
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