/*! 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 10 What Mathematica function is use... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 10

What Mathematica function is used to represent the inverse tangent function?

Short Answer

Expert verified
ArcTan

Step by step solution

01

Understanding Inverse Trigonometric Functions

Inverse trigonometric functions are used to obtain an angle from any of the trigonometric ratios. The inverse tangent function specifically takes a ratio (opposite/adjacent) and returns the angle whose tangent is that ratio.
02

Reviewing Mathematica Function Names

Mathematica uses specific names for various mathematical functions. It often follows a consistent naming convention where the 'Inverse' prefix is used along with the base trigonometric function name.
03

Identifying the Inverse Tangent Function

In Mathematica, the inverse tangent function is represented by the function name `ArcTan`. This function takes a number and returns the corresponding angle.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mathematica functions
Mathematica is a powerful tool for mathematical computations and symbolic processing. It comes with a range of built-in functions designed to handle various mathematical operations. These functions are named following specific conventions that make it easier to guess their purpose.
For instance, functions related to trigonometry have names that are intuitive. In many cases, inverse functions are named with the prefix 'Arc' followed by the base trigonometric function's name. This consistent naming style helps users find and apply functions without exhaustive searching.
The Mathematica function for inverse tangent follows this logic.
inverse trigonometric functions
Inverse trigonometric functions are essential in mathematics to find angles from trigonometric ratios. These functions include \(\text{ArcSin} \), \(\text{ArcCos} \), and \(\text{ArcTan} \), among others.
The primary use of these functions is to determine an angle when respective trigonometric values are known. They reverse the regular trigonometric functions like sine, cosine, and tangent.
For example, the inverse tangent function takes a ratio - typically the ratio of the opposite side to the adjacent side in a right triangle - and returns the angle whose tangent is that ratio.
ArcTan
In Mathematica, the inverse tangent function is implemented as `ArcTan`. This function is essential when you need to determine the angle from a given tangent value.
The \(\text{ArcTan[x]} \) function returns the angle whose tangent is \( x \). This can be particularly useful in solving trigonometric equations and in applications involving right triangles.
The naming of `ArcTan` is intuitive: 'Arc' prefixes indicate inversion of a trigonometric function, and 'Tan' stands for tangent. This makes it easy to remember and use in programming with Mathematica.

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

Determine the proper syntax for evaluating \(\lim _{x \rightarrow \pi / 2} \sin x\) and evaluate the limit.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Applied 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.