find the exact value do not use a calculator\n\ncsc\\(\\left(-\\frac{\\pi}{2}\\right)\\)\n\ncsc\\(\\left(-\\f…

Explanation:

Step1: Use the property of cosecant function

Recall that (\csc x=\frac{1}{\sin x}). So, (\csc\left(-\frac{\pi}{2}\right)=\frac{1}{\sin\left(-\frac{\pi}{2}\right)}).

Step2: Use the property of sine function

Since (\sin(-\alpha)=-\sin\alpha), then (\sin\left(-\frac{\pi}{2}\right)=-\sin\frac{\pi}{2}). And we know that (\sin\frac{\pi}{2} = 1), so (\sin\left(-\frac{\pi}{2}\right)=- 1).

Step3: Calculate the value of (\csc\left(-\frac{\pi}{2}\right))

Substitute (\sin\left(-\frac{\pi}{2}\right)=-1) into (\csc\left(-\frac{\pi}{2}\right)=\frac{1}{\sin\left(-\frac{\pi}{2}\right)}), we get (\csc\left(-\frac{\pi}{2}\right)=\frac{1}{-1}=-1).

Answer:

(-1)