/*! 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 33 Find a formula for \(\tan \left(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 33

Find a formula for \(\tan \left(\theta+\frac{\pi}{4}\right)\).

Short Answer

Expert verified
The formula for \(\tan \left(\theta+\frac{\pi}{4}\right)\) is \(\tan \left(\theta + \frac{\pi}{4}\right) = \frac{\tan(\theta) + 1}{1 - \tan(\theta)}\).

Step by step solution

01

Write down the tangent addition formula

We will use the tangent addition formula to find the formula for \(\tan \left(\theta+\frac{\pi}{4}\right)\): \[\tan(\alpha + \beta) = \frac{\tan(\alpha) + \tan(\beta)}{1 - \tan(\alpha) \tan(\beta)}\]
02

Substitute the provided values

Now, we will substitute \(\alpha = \theta\) and \(\beta = \frac{\pi}{4}\) into the formula: \[\tan \left(\theta + \frac{\pi}{4}\right) = \frac{\tan(\theta) + \tan\left(\frac{\pi}{4}\right)}{1 - \tan(\theta) \tan\left(\frac{\pi}{4}\right)}\]
03

Simplify the expression

Since we know that \(\tan\left(\frac{\pi}{4}\right) = 1\), we can simplify the expression: \[\tan \left(\theta + \frac{\pi}{4}\right) = \frac{\tan(\theta) + 1}{1 - \tan(\theta) \cdot 1}\] Finally, we can rewrite our expression in simpler form: \[\tan \left(\theta + \frac{\pi}{4}\right) = \frac{\tan(\theta) + 1}{1 - \tan(\theta)}\] Now we have found the formula for \(\tan \left(\theta+\frac{\pi}{4}\right)\).

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

Convert the polar coordinates given for each point to rectangular coordinates in the \(x y\) -plane. $$ r=12, \theta=\frac{11 \pi}{4} $$

Explain how the sine behaves with phase shifts of one-fourth its period, one- half its period, and all of its period, similarly to what was done for the cosine in the bulleted list that appears between Examples 6 and 7 .

What is the range of the function \(7 \cos \left(\frac{\pi}{2} x+\frac{6 \pi}{5}\right) ?\)

By what fraction of the period of \(6 \cos \left(\frac{\pi}{3} x\right)\) has the graph been shifted left to obtain the graph of \(6 \cos \left(\frac{\pi}{3} x+\frac{8 \pi}{5}\right) ?\)

Convert the rectangular coordinates given for each point to polar coordinates \(r\) and \(\theta .\) Use radians, and always choose the angle to be in the interval \((-\pi, \pi)\). $$ (3,2) $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.