Find sin(x-y) and tan(x-y) exactly without a calculator.

[Gretta99]

Find sin(x-y) and tan(x-y) exactly without a calculator.

cos(x)= -1/3 , tan(y)=1/2, x is a quadrant II Angle, y is a quadrant III angle.

I really have no idea how to start this. I tried making them triangles and then finding what the sides were, but I still don't know the values of x and y. Please help me get this started! I think that it might involve the difference quotient identity but I don't know how to apply it.

Thanks!

Michelle

 

[arthur ohlsten]

in second quadrant sketch a right triangle with hypoteneuse 3 adjacent side -1.
The opposite side is sqrt 8, and the angle is x

In third quadrant sketch a right triangle with adjacent side -1, opposite side -1
The hypoteneuse is sqrt 5 , and the angle is y

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sin [x-y] = sin x cosy - cos x sin y
all values from above triangles

tan [x-y] = sin [x-y] / cos [x - y]

cos [x-y] = cos x cos y + sin x sin y
sin [x-y] = sin x cos y - cos x sin y
all values from above triangles

please check math and trig relationships

Arthur