How do you evaluate cot[arccos (-4/5)] cot[arccos(−45)]?

1 Answer
Bdub
Oct 12, 2016

cot[arccos(-4/5)]=-4/3cot[arccos(−45)]=−43

Explanation:

cot[arccos(-4/5)]cot[arccos(−45)]-->restriction for arccos xarccosx is [0,pi][0,π].

Since the argument is negative that means our triangle is in quadrant two with the adjacent side -4 and hypotenuse 5. Hence this is a 3-4-5 triangle with the opposite side being 3.

Therefore cot thetacotθ = adjacent/opposite = a/o = -4/3ao=−43

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