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.)
Find the exact value of the trigonometric function
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trigonometry
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1Dear MOG, Welcome to math.SE. since you are a new user, we wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say what your thoughts on the problem are so far; this will prevent people from telling you things you already know, and help them write their answers at an appropriate level. Further, it would be better if you could typeset your problem so that it is easy for people to read. Kindly look http://meta.math.stackexchange.com/questions/107/faq-for-math-stackexchange/117#117 for more details. – 2012-10-29
2 Answers
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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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0Even 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](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference). – 2015-08-16