math question about triangles ooooo ahhhhh

the answer in the book is wrong.
You are correct.

I actually ran into this same thing later on in the book, it was giving the 6 ratios for a right triangle with 45 corners, the sides are 1, 1, and sqrt(2) once more they state sin is sqrt(2)/2 and cos is sqrt(2)/2 This shouldn't be the case, yet it printed it like that again, in a completely different chapter. I'm trying to reason why they did this the way they did, for instance if they are wrong, how did they reach that conclusion?

I am sorry, you were right but so was your book.

1/root2 = (1*root2)/(root2*root2) = root2/2

The author has rationalized the denominator (made the fraction so that the bottom is rational)

It is considered to be simplified if the demoninator is rational.

Oh, it's that one rule thingy where you can't have squareroot on the bottom of a fraction. aighty, wasn't sure, but i vaguely recall that being mentioned years ago, it is of course not present in the book so far as i see.

That is ok, you will remember it now. Glad I could help.

Thankyou kindly! I'll be sure to post more interesting trig questions as they emerge, but so far, when doing my math i come up short by 4 when the answer was in the 1000's, i think it's the rounding of the calculator on here, since i lack one that can do sec, csc, cot and their arc functions.

I have never owned or used a calculator that does any of those things.
The calculator on this site does have those functions but I haven't tried to use them.
If you use lots of decimal places in your working and only round at the very end you should not get many rounding discrepancies.

[input]simplify(sqrt(2)/2)[/input]

I am sorry but I believe this is incorrect.

root2 / 2 is regarded as the more simple form.

I thought you can't leave a square root in the denominator?

no, you are not supposed to, that is what I said.

Were you hoping to get a response from admin, I'm sorry I butted in if you were.

If you want an answer from admin it might be better if you start a new thread and adress it to admin in the title line. imo

all good, but yeah both of those are the same, except one is rational, the other irrational, and for all intents put the square root on the top, i was informed this today

The practice of rationalizing the denominator of the fraction relies on the following rules:

1. Both numerator and denominator are multiplied by denominator and the operation is repeated frequently until irrationality is fully eliminated.

2. If only a part of denominator is under radical sign, then irrationality is broken by multiplying both numerator and denominator by conjugate expression thus involving the formula a^2 - b^2. Once again, this operation is repeated as many times as it's necessary to break free of the radical.

Example: a/[sqrt(m) - sqrt(n)] = a[sqrt(m) + sqrt(n)]/[sqrt(m) - sqrt(n)]*[sqrt(m) + sqrt(n)] = a[sqrt(m) + sqrt(n)]/[m - n];

a/sqrt(n) = [a*sqrt(n)]/n