# pre calc

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Find the exact value of sin(x-y) if sinx=-3/5 in Quadrant III and cosy=5/13 in Quadrant I.

• pre calc -

If sin(x)=-3/5 in Q3, then
cos(x)=-4/5 (using cos²(x)=1-sin²(x))
Similarly,
cos(y)=5/13 in Q1 means sin(y)=12/13

sin(x-y)=sin(x)cos(y)-cos(x)sin(y)
=-3/5*5/13 - (-4/5)*12/13
=(-15+48)/65
=33/65

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