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!
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):
$\displaystyle \sin (x-y) = \sin x \cos y - \cos x \sin y$
$\displaystyle \cos (x + y) = \cos x \cos y - \sin x \sin y$