/*! 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 46 Use the value of the trigonometr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 46

Use the value of the trigonometric function to evaluate the indicated functions. \(\cos t=-\frac{3}{4}\) (a) \(\cos (-t)\) (b) \(\sec (-t)\)

Short Answer

Expert verified
The value of \(\cos (-t)\) is -\frac{3}{4} and the value of \(\sec (-t)\) is -\frac{4}{3}.

Step by step solution

01

Evaluate \(\cos (-t)\)

The cosine function has a property known as being 'even'. This means that \(\cos (-t) = \cos t\). Therefore, since \(\cos t = -\frac{3}{4}\), we can say that \(\cos (-t) = -\frac{3}{4}\).
02

Evaluate \(\sec (-t)\)

The secant function \(\sec (x)\) is defined as the reciprocal of the cosine function, or \(\sec (x) = \frac{1}{\cos (x)}\). Therefore, using the value for \(\cos t = -\frac{3}{4}\) that we already have, we can find that \(\sec (-t) = -\frac{4}{3}\).

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

Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \csc x=-\frac{2 \sqrt{3}}{3} $$

Sketch the graph of the function. Include two full periods. $$ y=3 \cot 2 x $$

Evaluate the expression without using a calculator. $$ \arctan \sqrt{3} $$

Sketch the graph of the function. Include two full periods. $$ y=2 \sec (x+\pi) $$

Use a graphing utility to graph the two equations in the same viewing window. Use the graphs to determine whether the expressions are equivalent. Verify the results algebraically. $$ y_{1}=\sec ^{2} x-1, \quad y_{2}=\tan ^{2} x $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

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.