/*! 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 6 Evaluate \(\tan \left(\tan ^{-1}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 6

Evaluate \(\tan \left(\tan ^{-1} 5\right)\).

Short Answer

Expert verified
In conclusion, we find that \(\tan(\tan^{-1}(5)) = 5\).

Step by step solution

01

Find the angle whose tangent is 5

First, we need to find the angle (in radians or degrees) whose tangent is 5. To do this, we will use the inverse tangent function \(\tan^{-1}(x)\): \(\theta = \tan^{-1}(5)\)
02

Evaluate the tangent of the angle found in step 1

Now that we have the angle, we can find the tangent of it. Since the angle is the output of the inverse tangent function of 5 (from the previous step), the tangent of this angle must be equal to 5: \(\tan(\theta) = \tan(\tan^{-1}(5)) = 5\)
03

Write the final answer

In conclusion, we find that \(\tan(\tan^{-1}(5)) = 5\).

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

Evaluate \(\cos \left(\cos ^{-1} \frac{1}{4}\right)\)

Evaluate \(\tan \left(-\tan ^{-1} \frac{7}{11}\right)\)

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with \(\tan u=-2\) and \(\tan v=-3\) Find exact expressions for the indicated quantities. $$ \sin \left(\frac{\pi}{2}-v\right) $$

Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with \(\tan u=-2\) and \(\tan v=-3\) Find exact expressions for the indicated quantities. $$ \tan (-v) $$

Suppose a 19 -foot ladder is leaning against a wall, making a \(71^{\circ}\) angle with the ground (as measured from a perpendicular line from the base of the ladder to the wall). How high up the wall is the end of the ladder?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.