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when sinx=(-8/17) and x lies in quadrant 3 and cosy=(-4/5) and y lies in quadrant 2, what is cos(x-y)?

when sinx=(-8/17) and x lies in quadrant 3 and cosy=(-4/5) and y lies in quadrant 2, what is cos(x-y)?

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1 Answers

abc
33 Points
6 years ago
when sinx= (-8/17) ,we know that the hypotenuse is 17 and one side is 8 . so by pythagoras theorem,17^2=8^2+a^2
so a^2=225
a=15
and similarly,
in the other triangle 3rd side is 3
so putting values
cos(x-y)=cosx cosy - sinx siny............. (identity)
cos(x-y)=(-4/5)*(-15/17)-(3/5)*(-8/17) ….....................(since sinx is  negative x-axis/ negative hypo.)
cos(x-y)=36/85

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