SOLUTION: How do you solve arccos(cot(5)) and state which quadrant it is in? Explain please.

Question 668561: How do you solve arccos(cot(5)) and state which quadrant it is in? Explain please.
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
First off, what is cot(x)? It is cos(x)/sin(x). We know that the arcos(cos(x)) = x. While the arccos(sin(x)) = sqrt(1-x^2) (think of pythagorean theorem with x, sqrt(1-x^2) and 1) So we have that arccos(cot(x)) = x/sqrt(1-x^2)
When we consider that 5 is in radians, then we get that arccos(cot(x)) = 1.87, so it is slightly larger than pi/2 and thus in Q2.
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