/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 39 Evaluate the trigonometric funct... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 39

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

Short Answer

Expert verified
The secant of \( \frac{3 \pi}{2} \) is undefined.

Step by step solution

01

Identify the Quadrant and Reference Angle

The angle \( \frac{3 \pi}{2} \) lies in the third quadrant of the unit circle (since \( \pi < \frac{3 \pi}{2} < \frac{2 \pi}{1} \)). Here, the reference angle will be the same since we're dealing directly with quadrant angles.
02

Find the Cosine of the Reference Angle

On the unit circle, the cosine of an angle can be thought of as the x-coordinate of the point where the terminal side of the angle meets the unit circle. For \( \frac{3 \pi}{2} \), this x-coordinate is 0.
03

Evaluate the Secant Function

Since secant is the reciprocal of cosine, we need to calculate \( \sec(\frac{3 \pi}{2}) = \frac{1}{\cos(\frac{3 \pi}{2})} \). But as \( \cos(\frac{3 \pi}{2}) = 0 \), its reciprocal, or the secant, is undefined. That is because division by zero is undefined in mathematical operations.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the distance between Dallas, Texas, whose latitude is \(32^{\circ} 47^{\prime} 39^{\prime \prime} \mathrm{N}\) and Omaha, Nebraska, whose latitude is \(41^{\circ} 15^{\prime} 50^{\prime \prime} \mathrm{N}\) Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (Omaha is due north of Dallas).

Define the inverse secant function by restricting the domain of the secant function to the intervals \([0, \pi / 2)\) and \((\pi / 2, \pi],\) and sketch the graph of the inverse trigonometric function.

Fill in the blank. If not possible, state the reason. $$\text { As } x \rightarrow 1^{-}, \text {the value of } \arccos x \rightarrow\text { _____ } .$$

Find a model for simple harmonic motion satisfying the specified conditions. Displacement \((t=0)\) 2 feet Amplitude 2 feet Period 10 seconds

Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\) (a) \(x \rightarrow\left(\frac{\pi}{2}\right)^{+}\) (b) \(x \rightarrow\left(\frac{\pi}{2}\right)^{-}\) (c) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{+}\) (d) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{-}\) $$f(x)=\tan x$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.