Question

Inverse trigo help!

Answer 1

\[\Huge \cot^{-1}7 + \cot^{-1}8+\cot^{-1}18=?\]

Answer 2

I know that the range of arccot is (0,pi) so we have to convert all those values..
\[\Huge \cot^{-1}7=\cot^{-1}(7-2\pi)\]
similarly the other values..if im right?
\[\Huge \cot^{-1}8=\cot^{-1}(8-2\pi)\]
\[\Huge \cot^{-1}18=\cot^{-1}(18-6 \pi)\]

Answer 3

just an attempt though

Answer 4

I don't think you have to convert anything here. The range of inverse cotangent doesn't matter here. If anything it tells you that \(0<\cot^{-1}7<\pi\), but that's about it.

Answer 5

And besides, that's not the right range. The range for arccot is \(\left(-\dfrac{\pi}{2},0\right)\cup\left(0,\dfrac{\pi}{2}\right)\)

Answer 6

yeah i know

Answer 7

how do we know the value of arccot7

Answer 8

Well, I'd use a calculator because I'm not familiar with the identities involving inverse trig functions.

According to Wolfram, your value is equivalent to \(\cot^{-1}3\approx0.32175\).

Answer 9

im not given calc during exams .-. any way to approximate it?

Answer 10

Not that I know of, but then again, there may be identities you're expected to know in order to figure this out.