# Find the exact value of the trigonometric function

Find the exact value of $$\cot(v-u)$$ given that $\sin u=−3/5$ and $\cos v = − 7/25$ (Both $u$ and $v$ are in Quadrant III.)

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Please don't just dump problems here --- tell us why you are interested in the question, what you know about it, where you get stuck in solving it, and so on. – Gerry Myerson Oct 29 '12 at 2:13

Some hints:

Do you know a formula relating the cotangent to the sine and cosine?

Do you know formulas relating $\sin(A+B)$ and $\cos(A+B)$ to $\sin A,\sin B,\cos A, \cos B$?

Do you know a formula relating $\sin C$ and $\cos C$?

Do you know which trig functions are positive in which quadrants?

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Hint: Apply $$\sin(A+B)=\sin A \cos B+\cos A \sin B$$ $$\cos(A+B)=\cos A \cos B- \sin A \sin B$$

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Even if it was meant to be a hint, you should give some more detail. For example, the OP has to use the negative version of this rule, and the OP has to know that $\cot(x)=\frac{\cos(x)}{\sin(x)}$. Otherwise the answer won't make that much sense. Further, please use LaTeX next time to format your formulas, there is a guide on meta. – wythagoras Aug 16 at 5:49