To solve for [tex]\(\csc\left(\frac{\pi}{2}\right)\)[/tex], we need to understand the cosecant function. The cosecant function is the reciprocal of the sine function. In mathematical terms:
[tex]\[
\csc(x) = \frac{1}{\sin(x)}
\][/tex]
Given the angle [tex]\(\frac{\pi}{2}\)[/tex], we first need to determine the value of [tex]\(\sin\left(\frac{\pi}{2}\right)\)[/tex]. The sine of [tex]\(\frac{\pi}{2}\)[/tex] is:
[tex]\[
\sin\left(\frac{\pi}{2}\right) = 1
\][/tex]
Now, we can find [tex]\(\csc\left(\frac{\pi}{2}\right)\)[/tex]:
[tex]\[
\csc\left(\frac{\pi}{2}\right) = \frac{1}{\sin\left(\frac{\pi}{2}\right)} = \frac{1}{1} = 1
\][/tex]
Hence, the correct answer is:
[tex]\[
\csc\left(\frac{\pi}{2}\right) = 1 \quad \text{(Option C)}
\][/tex]
