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Chapter 5: Problem 45

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

Short Answer

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

Step by step solution

01

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 \(\cos \frac{3 \pi}{2}\).
02

Calculate cosine of the given quadrant angle

The angle \(\frac{3\pi}{2}\) is equivalent to 270掳 in degrees. By considering the unit circle, it is known that at 270掳, the x-value (which represents cos) is 0 and the y-value (which represents sin) is -1. Therefore, \(\cos \frac{3 \pi}{2} = 0 \).
03

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 \(\sec \frac{3 \pi}{2}= 1/0 \).

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Most popular questions from this chapter

Your classmate uses a calculator to evaluate \(\tan (\pi / 2)\) and gets a result of 0.0274224385 Describe the error.

Determine whether the statement is true or false. Justify your answer. \(\arctan x=\frac{\arcsin x}{\arccos x}\)

Solve the equation. Round your answer to three decimal places, if necessary. $$3 x-7=14$$

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Find the exact value of each function for the given angle for \(f(\theta)=\sin \theta\) and \(g(\theta)=\cos \theta .\) Do not use a calculator. (a) \((f+g)(\theta)\) (b) \((g-f)(\theta)\) (c) \([g(\theta)]^{2}\) (d) \((f g)(\theta)\) (e) \(f(2 \theta)\) (f) \(g(-\boldsymbol{\theta})\) $$\theta=5 \pi / 6$$
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