Chapter 13.8, Problem 20PPSE

Solution

To find: The value of $\sec \left(-\frac{3\pi }{2}\right)$ with the help of a calculator and round the answer to the nearest thousandths.

The value of $\sec \left(2.5\right)=-1.248$ rounded to nearest thousandths.

Given:

The trigonometric expression to evaluate is $\sec \left(-\frac{3\pi }{2}\right)$ .

Calculation:

Since the secant function is a reciprocal function of cosine trigonometric function except odd multiple of $\frac{\pi }{2}$ where it is not defined. Therefore, the value of $\sec \left(-\frac{3\pi }{2}\right)$ is not defined because the argument of $\sec \left(-\frac{3\pi }{2}\right)$ is odd multiple of $\frac{\pi }{2}$ .

Conclusion:

The value of $\sec \left(-\frac{3\pi }{2}\right)$ is not defined.