Problem 45 - Algebra and Trigonometry Real Mathematics, Real People

Question

Evaluate the trigonometric function of the quadrant angle, if possible. $$\sec \frac{3 \pi}{2}$$

Step-by-Step Solution

Answer

The secant of the angle is undefined because we are trying to divide by zero. In mathematics, division by zero is not defined.

Step 1: Understand the secant function

The secant function, sec(x), is the reciprocal of the cosine function. It's defined as sec(x)=1/cos(x). Therefore, to evaluate \(\sec \frac{3 \pi}{2}\), we first need to determine the value of \(\cos \frac{3 \pi}{2}\).

Step 2: Calculate cosine of the given quadrant angle

The angle \(\frac{3\pi}{2}\) is equivalent to 270° in degrees. By considering the unit circle, it is known that at 270°, the x-value (which represents cos) is 0 and the y-value (which represents sin) is -1. Therefore, \(\cos \frac{3 \pi}{2} = 0 \).

Step 3: Evaluate the secant function

The secant value is given by the reciprocal of the cosine value. Since the cosine of \(\frac{3\pi}{2}\) is 0, the secant of this angle is \(\sec \frac{3 \pi}{2}= 1/0 \).