Question

Without using a calculator, find the exact value of cos^-1(cos(17pi/5)). Thanks for the help :)

Answer 1

what's your knowing about \[Cos(x)\]and\[Cos^{-1} (x)\]

Answer 2

simplify arccos(cos(17pi/5))

Answer 3

which reduces to arccos(cos(7pi/5))

Answer 4

arcsin(sin(x)) = x
and
arccos(cos(x)) = x

Answer 5

^^^ is true, IF x is in the range of the inverse function. If not, you need the angle that has the same function value AND is in the range. (Just a little caveat.)

Answer 6

Same question was asked yesterday:
http://openstudy.com/study#/updates/52129ad4e4b0450ed75d8324

and note that 7pi/5 is NOT in the range of y=arccos(x)