Question

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

Answer 1

\[\cos^{-1}[\cos{(\frac{17\pi}{5})]}=\]

Hopefully you recognize that you have what you started with, but reduced to be within the normal range. How many times can you subtract 2pi from 17pi/5 and stay > 0?

Answer 2

your job is only to find the angle in the interval \([0,\pi]\) that has the same cosine as \(\frac{17\pi}{5}\)

Answer 3

@whpalmer4 i think this one is a little trickier than that, because if you subtract \(2\pi\) you get \(\frac{7\pi}{5}\) which is still not quite good enough

Answer 4

Wasn't intending that to be the whole solution, just a starting point

Answer 5

And perhaps not artfully described, at that!

Answer 6

speaking of "art" that is truly ugly

Answer 7

I'm surprised you don't have a library of drawings to attach by this point!

Answer 8

actually i usually attach this but it is not helpful here

Answer 9

find \(\frac{17\pi}{5}\)
in my ugly picture it is this

Answer 10

now move directly north, so the cosine will be the same, but will be in the interval \([0,\pi]\)

Answer 11

2pi/3