Question

find the range of the function 1/1-sinx

Answer 1

can't be 0

Answer 2

\(\large \text{use the fact that}\)
\(\large\tt \begin{align} \color{black}{
-1\leq sinx \leq 1\\~\\~\\~\\
f(x)=\dfrac{1}{1-sinx}\\~\\
f(270^{\circ})=\dfrac{1}{1-(-1)}\\~\\
~~~~~~~~~~~=\dfrac{1}{1-(-1)}\\~\\
~~~~~~~~~~~=\dfrac{1}{2}\\~\\~\\~\\
f(x)=\dfrac{1}{1-sinx}\\~\\
f(90^{\circ})=\dfrac{1}{1-1}\\~\\
~~~~~~~~~=\dfrac{1}{0}\\~\\
~~~~~~~~~=\infty\\~\\~\\~\\
R_{f(x)}=[\dfrac{1}{2},\infty)
}\end{align}\)