Question

can anyone please explain why the exact value of cot(13pi/8) is 1-(2)^1/2??

Answer 1

Let's see, cot (13pi/8) is same as cot(5pi/8) (periodic in pi) so 1/Tan 5pi/8 and u should be able to break that up....

Answer 2

half angle formula for tangent may help

Answer 3

ick ugly algebra, but i think it can be done. first of all
\[\cot(\frac{13\pi}{8})=-\tan(\frac{\pi}{8})\] which doesn't really make the calculation any easier, because you still have to use the half angle formula

Answer 4

formula for
\[\tan(\frac{x}{2})=\frac{\tan(x)}{1+\sqrt{1+\tan^2(x)}}\] should do it, with
\[x=\frac{\pi}{4}\] and
\[\tan(\frac{\pi}{4})=1\] , rationalize the denominator and you will get your answer. i can work it out if you like

Answer 5

please do. its my first time with these formulas

Answer 6

if so, then the answer is \[\sqrt{2} - 1\] right? but my calculator says otherwise