# Thread: Just a few doubts

1. ## Just a few doubts

Determine if True or False

A. sin(sin inverse x) = x for all real numbers x
Not sure...(what is it asking?)sin of sin inverse x(can any explain what this means?)

B. The graph of y = tan inverse x has two horizontal asymptotes
True...i am sure

C. 2cosxsinx - cosx = 0
Find X between [0,2pi)

x = pi/2, 3pi/2

I am also sure about number 3.

Wanted to check.

Thanks for any help...

2. $\displaystyle \sin \left({\sin^{-1} x}\right)$ does not equal $\displaystyle x$ for all $\displaystyle x$.

Because $\displaystyle \sin^{-1} x$ is not defined for $\displaystyle x < -1$ or $\displaystyle x > 1$.

3. Originally Posted by Matt Westwood
$\displaystyle \sin \left({\sin^{-1} x}\right)$ does not equal $\displaystyle x$ for all $\displaystyle x$.

Because $\displaystyle \sin^{-1} x$ is not defined for $\displaystyle x < -1$ or $\displaystyle x > 1$.
alright, but i do not understand what
$\displaystyle \sin \left({\sin^{-1} x}\right)$

is saying

Thanks for help though

4. Okay, let's say you have $\displaystyle y = \sin^{-1} x$.

That is, $\displaystyle y$ is the "inverse sine" of $\displaystyle x$.

That means, "What value of $\displaystyle y$ do you have to take the sine of to get $\displaystyle x$?

That is, it's doing $\displaystyle x = \sin y$ but this time you know what $\displaystyle x$ is and you want to find $\displaystyle y$.

So doing $\displaystyle \sin \left({\sin^{-1} x}\right)$ is like saying:

"We've got this value $\displaystyle x$, and we find the number it is the sine of. Then we take this number and take its sine."

You seem to understand what $\displaystyle \tan^{-1} x$ is, you could do question B.

The trouble is here, is that not all numbers are the sine of another number, because the only possible values for the sine of a number are between -1 and 1.

So if someone says: "What's the inverse sine of 2?" you'd reply "Don't be silly, it doesn't exist." (Not at this level of mathematics anyway.)