Back To Course

AP Calculus AB & BC: Homework Help Resource17 chapters | 139 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Log in here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

The arctan, or arctangent, is the inverse function of the tangent function. This lesson will define the arctan, describe its function, and take you through some examples.

Every mathematical function has an inverse. Even simple operations such as addition and multiplication have inverses - subtraction and division. The **arctan** is the inverse of the tangent function and is used to compute the angle measure from the tangent ratio of a right triangle, designated by the formula:

tan = opposite / adjacent

The term 'arc' is used because when measuring an angle in **radians**, the arc length of a portion of a circle bisected by an angle (with the vertex at the center of the circle) equals the angle measure. The **radian** is the standard unit of measurement for an angle and is equal to approximately 57 degrees. It is based on the radius of a circle.

**Trigonometric functions** can be used to define values related to a right triangle. Practically, these functions can be used to determine heights of objects or distances that are difficult to measure. These measurements are determined using the measure of one angle (not the right angle) and a ratio of two sides of the triangle. Trigonometric functions are determined by the sides of the triangle that are used in the ratio of these formulas:

- sine = opposite / hypotenuse
- cosine = adjacent / hypotenuse
- tangent = opposite / adjacent

The inverse of these functions can be used to determine the angle measures when the sides of the triangle are known. You can use the **arctan** to determine an angle measure when the side opposite and the side adjacent to the angle are known. The arctan has practical applications in architecture, building, landscaping, physics, and engineering, among other scientific and mathematical areas.

The best method to use to determine the arctan is a **scientific calculator**. The button for arctan should be above the tangent on the calculator. A table of data can also be used to determine the arctan; however, this can be a tedious and a cumbersome method, but it is effective if a scientific calculator is not available.

Next, we'll look at some examples where the arctan is used to find the angle measure.

In this first example, let's find the angle measure of Î¸:

Remember, the arctan is the trigonometric function that you can use to determine an angle measure when you know the side opposite and the side adjacent to the angle measure you are trying to find.

The equation will look like this:

arctanÎ¸ = opposite / adjacent

arctanÎ¸ = 15 / 23

arctanÎ¸ = 0.65

Î¸ = 33°

In this second example, we'll find the measure of angleÎ¸:

arctanÎ¸ = opposite / adjacent

arctanÎ¸ = 3 / 2

arctanÎ¸ = 1.5

Î¸ = 56°

In our final example, we'll use a wheelchair ramp that rises 6 vertical feet over a distance of 25 feet. What is the angle measure of the incline of the ramp?

arctanÎ¸ = opposite / adjacent

arctanÎ¸ = 6 / 25

arctanÎ¸ = 0.24

Î¸ = 13°

The **arctan** is the inverse trigonometric function of the **tangent function**, which is the ratio of the side opposite an angle divided by the side adjacent to the angle. The arctan function is used to determine the angle measures of a right triangle when the legs of the triangle are known. It has practical applications in architecture, engineering, and physics, along with other sciences. The arctan is computed using a scientific calculator or a table of data.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Log in here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
8 in chapter 16 of the course:

Back To Course

AP Calculus AB & BC: Homework Help Resource17 chapters | 139 lessons

- How to Solve Visualizing Geometry Problems 10:41
- How to Calculate the Volumes of Basic Shapes 7:17
- Finding Distance with the Pythagorean Theorem 6:54
- Trigonometry: Sine and Cosine 7:26
- Trigonometry and the Pythagorean Theorem 4:14
- Arccosine: Definition & Overview
- Arcsine: Definition & Overview
- Arctan: Definition, Function & Formula 3:54
- Go to Geometry and Trigonometry in AP Calculus: Homework Help Resource

- SIE Exam Study Guide
- Indiana Real Estate Broker Exam Study Guide
- Grammar & Sentence Structure Lesson Plans
- Foundations of Science Lesson Plans
- Career, Life, & Technical Skills Lesson Plans
- Business Costs, Taxes & Inventory Valuations
- Using Math for Financial Analysis
- Assessments in Health Education Programs
- Governmental Health Regulations
- Understanding Health Education Programs
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- What is Deadlock? - Definition, Examples & Avoidance
- El Hombre que se Convirtio en Perro: Author, Summary & Theme
- Achilles in The Iliad: Character Analysis & Description
- A Wrinkle in Time Chapter 5 Summary
- Roald Dahl Project Ideas
- Media Literacy Activities for High School
- Letter M Activities
- Quiz & Worksheet - Shang Dynasty Religion & Culture
- Quiz & Worksheet - Alternative Assessment Types
- Quiz & Worksheet - Population Composition
- Quiz & Worksheet - Minimalist Painters
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- 3rd Grade Math Worksheets & Printables
- Guided Reading Lesson Plans

- Business 308: Globalization & International Management
- Providing After-Sales Customer Service
- Senior Professional in Human Resources - International (SPHRi): Exam Prep & Study Guide
- Remedial Precalculus
- MTLE Physical Education: Practice & Study Guide
- Absolute Value: Homeschool Curriculum
- Industrialization From 1870-1900: Homework Help
- Quiz & Worksheet - RNA in Protein Synthesis
- Quiz & Worksheet - Working in a Team Environment
- Quiz & Worksheet - Characteristics of a Market System
- Quiz & Worksheet - Characteristics of an Amphibian
- Quiz & Worksheet - Principle of Management by Exception

- Do Bacteria Cells Have DNA?
- The Crucible Discussion Questions
- 7th Grade Writing Prompts
- Oregon Teacher Professional Development
- Geometry Math Games
- How to Learn French Quickly
- 1st Grade Science Projects
- Study.com's Top Online Business Management Training Courses
- Homeschooling in North Dakota
- Environmental Science Projects
- Journal Writing Prompts
- Common Core Standards & English Language Learners

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject