Question

what is the DOMAIN of :
f(x) = (-cosx) / 2(rtsqr(1-sinx))

Answer 1

\[f(x) = \frac{-cosx}{2 \sqrt{1 - sinx}}\]

Here the terms inside the square toot must not be negative because square root of negative is not defined so:

\[\large 1- sinx \ge 0\]

Or:

\[sinx \le 1\]

Here x can take values for that sinx will not less than or equal to one this is the only condition here..

Answer 2

just for completing waterineyes statement :

\(\sin x≤1\) is true always...but ..we should consider the division by zero...so we must have

\(\sin x≠1\) so the domain is

\[R-\left\{ 2n\pi+\frac{\pi}{2} \right\} \ \ n=0,1,2,3,...\]

Answer 3

wait what happens to the cos and 2?