If sinx=-12/13 and x is in Quadrant IV, and cosy=-7/25, y in Quadrant II, find the value of sin(x-y) and cos(x+y).

Thank you!

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- Apr 6th 2008, 03:15 PMkelsey3Need help!....again. Evaluating a trig function
If sinx=-12/13 and x is in Quadrant IV, and cosy=-7/25, y in Quadrant II, find the value of sin(x-y) and cos(x+y).

Thank you! - Apr 6th 2008, 03:24 PMo_O
Draw the triangles out in both quadrants. Use pythagoras' theorem to solve for the hypotenuse of both triangles. Now you have all the necessary information to get sinx, cosx, sin y, and cos y. With these values, simply plug them into the formulae for sin(x-y) and cos(x+y):

$\displaystyle \sin (x-y) = \sin x \cos y - \cos x \sin y$

$\displaystyle \cos (x + y) = \cos x \cos y - \sin x \sin y$ - Apr 6th 2008, 03:39 PMkelsey3
Thank you much! Does cos(x+y)= -288/325 and sin(x-y)=204/325 sound right?

- Apr 6th 2008, 03:57 PMo_O
Sorry, I didn't mean hypotenuse earlier.

Hmm. That doesn't seem right. What did you get for sinx, cosx, siny, and siny? - Apr 6th 2008, 04:00 PMkelsey3
sinx= -12/13

siny= -24/25

cosx= 5/13

cosy= -7/25 - Apr 6th 2008, 04:03 PMo_O
siny shouldn't be negative. It's in quadrant II so siny must be positive while cosy must be negative. Hope that works out for ya!