How do i find cos[arctan(3/5)] ?

I know I need to set up some kind of triangle diagram, but I don't know how or what to do next. I am not allowed to use a calculator.

Thanks to anyone that tries to help me.

--Cori

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- Aug 26th 2007, 09:43 PMliz155How do I find cos[arctan(3/5)] ?
How do i find cos[arctan(3/5)] ?

I know I need to set up some kind of triangle diagram, but I don't know how or what to do next. I am not allowed to use a calculator.

Thanks to anyone that tries to help me.

--Cori - Aug 26th 2007, 09:52 PMJhevon
Let $\displaystyle \arctan \left( \frac {3}{5} \right) = \theta \implies \tan \theta = \frac {3}{5}$

Thus we can set up a right-triangle and label one of the acute angles "theta" and fill in the sides accordingly. (tangent = opposite/adjacent). we can use Pythagoras' theorem to find the length of the hypotenuse, which here is $\displaystyle \sqrt {34}$

Thus we can say, $\displaystyle \cos \left[ \arctan \left( \frac {3}{5} \right) \right] = \cos \theta = $ ?

It shouldn't be too hard for you to finish, right? - Aug 26th 2007, 10:03 PMliz155
Since cos= adjacent over hypotenuse...Would the answer be 5/sqrt(34)?

Thanks so much for your help and the great picture!!!:) - Aug 26th 2007, 10:04 PMJhevon
- Aug 26th 2007, 10:13 PMliz155
Thanks again! I really understand it now.:)

- Aug 26th 2007, 10:14 PMJhevon
- Aug 27th 2007, 06:00 AMKrizalid