# `sec(arctan(3x))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

### Textbook Question

Chapter 4, 4.7 - Problem 68 - Precalculus (3rd Edition, Ron Larson).
See all solutions for this textbook.

balajia | College Teacher | (Level 1) eNoter

Posted on

Taking 3x as oppsite side and 1 as the adjacent side,the hypotenuse will be equal to `sqrt(9x^2+1).`

So `tan^-1(3x)=sec^-1((sqrt(9x^2+1))/1)`

`sec(tan^(-1)(3x))=sec(sec^(-1)(sqrt(9x^2+1)))`

`=sqrt(9x^2+1)`
The passage contains a mathematical question and its solution, specifically dealing with an algebraic expression equivalent to a trigonometric function.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# `sec(arctan(3x))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

### Textbook Question

Chapter 4, 4.7 - Problem 68 - Precalculus (3rd Edition, Ron Larson).
See all solutions for this textbook.

balajia | College Teacher | (Level 1) eNoter

Posted on

Taking 3x as oppsite side and 1 as the adjacent side,the hypotenuse will be equal to `sqrt(9x^2+1).`

So `tan^-1(3x)=sec^-1((sqrt(9x^2+1))/1)`

`sec(tan^(-1)(3x))=sec(sec^(-1)(sqrt(9x^2+1)))`

`=sqrt(9x^2+1)`
user
The passage contains a mathematical question and its solution, specifically dealing with an algebraic expression equivalent to a trigonometric function.

TYPE: SINGLE_QUESTION_WITH_ANSWER