Step 1 :The limit as x approaches -π/2 from the right is asking for the value of the function as x gets very close to -π/2, but is still slightly greater than -π/2. Looking at the definition of the function, we see that for -π/2 < x < π/2, the function is defined as cos(x). Therefore, we need to find the value of cos(x) as x approaches -π/2 from the right.
Step 2 :The value of cos(x) as x approaches -π/2 from the right is approximately 0. This is because the cosine of -π/2 is 0. Therefore, the limit as x approaches -π/2 from the right of the function f(x) is 0.
Step 3 :Final Answer: \(\boxed{0}\)