Question

exact value of cot^-1(cot(13pi/9))

Answer 1

\[\cot ^-1(\cot (\frac{ 13\pi }{ 9}))\]

Answer 2

on the unit circle

Answer 3

you want the exact value?

Answer 4

=\[\frac{ 1 }{ \cot(\frac{ 13\pi }{ 9 }) }\]=\[\frac{ 1 }{ \cot(\frac{ 17\pi }{ 18}+\frac{ \pi }{ 2 })}\] using the formula cot(a+b)=(cotacotb-1)/cot(a)+cot(b)=
\[\frac{ \cot \frac{ \pi }{ 2 } +\cot \frac{ 17\pi }{ 18 }}{ \cot \frac{ \pi }{ 2 }\cot \frac{ 17\pi }{18 }-1}\]
=\[-\cot \frac{ 17\pi }{ 18}=-\cot(\frac{ 18\pi }{ 18 }-\frac{ \pi }{ 18 })\]

Answer 5

=\[-\cot(\pi-\frac{ \pi }{ 18 })=\cot(\frac{ \pi }{ 18 })\]