Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Trigonometry/Calc question?
My math professor posted a notice for an upcoming calc final.
He said
"
Class,
If you get an indefinite integral that contains root(sin^2(x)) or some other trigonometric function, in principle that is equal to the absolute value of the trigonometric function, i.e., root(sin^2(x))=|sin(x)|.
However,although it is incorrect in general, in the final exam if you get an indefinite integral that contains such a root, you can ignore the absolute value, i.e., root(sin^2(x))=sin(x). Do thing only if the integral is indefinite!
This will lead to a correct answer assumption that the trig function is positive on the interval of interest.".
Not entirely sure what he's trying to say.
Like if the trig function is positive on the interval, why does it matter if I have the absolute value sign or not? Also why does this only apply to indefinite integrals? Might be misreading things but I don't entirely get what he's trying to say.
1 Answer
- ?Lv 54 years ago
When we take the sq. root or even roots, for example Vx^2 = I x I, and I x I = x if x>= 0 or IxI = - x if x <0 because we really don't know x is a positive or a negative number. But in trig, we don't need the absolute symbol because we do have the given interval for the problem. For example : 0 < x < 90 , in this interval we know sin x always is a positive number. That is why we ignore the absolute value and the thing : Vsin^2x = I sin x I and I sin x I = sin x if 0 <= x <= 180 and
I sin x I = - sin x if 180 <= x <= 360 . In short, when you take the sq.root for trig. fuctions, you omit the absolute value.