How to find the exact value of cos(cos-1 pi) using calculator??? I keep getting error.

Question

phi · Answer

Are you sure the problem isn't

$$ \cos^{-1}( \cos( \pi)) $$

the cosine of an angle gives you a number between -1  and +1
the inverse cosine of a number (if that number is between -1 and +1)  gives you an angle.

notice that pi is bigger than +1,  and the inverse cosine has no (real) answer.  In other words, there is no angle where the cosine(angle) = 3.14  (all angles will have a cosine between -1 and +1)

anonymous · Answer

So in that case would it be 'Not defined'? My teacher gave me this problem maybe it was her mistake.

phi · Answer

If the problem is
$$ \cos^{-1}( \cos( \pi)) $$
you don't need a calculator.  the cosine of pi  is a number (-1, but we don't need to know that).  then the inverse cosine of that number returns back  pi

if the problem is as stated,  there is no real solution.

anonymous · Answer

Thank you!