/*! 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 1 Coterminal Angles Explain how to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 1

Coterminal Angles Explain how to find coterminal angles in degrees.

Short Answer

Expert verified
Coterminal angles are found by adding or subtracting multiples of 360 degrees to or from the given angle.

Step by step solution

01

Understanding Coterminal Angles

Coterminal angles are those that share an initial side and a terminal side. The circle of angles repeats every 360 degrees so to find a coterminal angle to a given angle, one can add or subtract 360 degrees.
02

Find a Positive Coterminal Angle

To find a positive coterminal angle with a given angle, add 360 degrees to the given angle until the result is positive.
03

Find a Negative Coterminal Angle

To find a negative coterminal angle with a given angle, subtract 360 degrees from the given angle until the result is negative.

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.

Degrees in a Circle
A circle, in terms of angles, is a complete rotation that equals 360 degrees. This full circle can be split into smaller parts, each part representing an angle. Understanding this basic division is key to grasping the concept of angles and coterminal angles.
Think of the circle as a pizza cut into 360 tiny slices, where each slice measures 1 degree. When you're dealing with angles, you're essentially dealing with how many of these slices you've counted off.
  • A complete rotation around the circle equals 360 slices (degrees), bringing you back to your starting point.
  • This cyclic nature makes angles like 0掳, 360掳, 720掳, etc., share the same position, since they all represent full rotations.
Recognizing the 360-degree cycle is crucial, as it helps in identifying coterminal angles鈥攖hose angles that appear identical on the circle despite differing in measure by full rotations.
Positive Angle
When dealing with angles, a positive angle is one that is measured by rotating counterclockwise from the initial side. This is the conventional direction for measuring angles and is important when discussing coterminal angles.
To find a positive coterminal angle, you start with your angle, and if it's negative or you need another positive angle, you add 360 degrees. This essentially moves the angle through another full cycle around the circle.
  • For instance, if you start at -30掳, adding 360掳 results in a positive angle of 330掳.
  • If your initial angle is already positive, say 45掳, adding 360掳 gives you 405掳, another coterminal angle.
  • This method highlights the repetitive nature of angles on the circle.
Using counterclockwise rotation and addition of full cycles helps in maintaining or finding positive equivalent positions on the circle.
Negative Angle
Conversely, a negative angle is measured by rotating clockwise from the initial side. This rotates in the opposite direction compared to positive angles and adds diversity in how angles can be represented.
Finding a negative coterminal angle involves subtracting 360 degrees. This helpful trick lets you cycle backward to find an angle that looks the same from a geometric perspective.
  • Suppose we start with 30掳, to find a negative coterminal angle, you subtract 360掳 to get -330掳.
  • If you have a negative angle already, like -45掳, subtracting another 360掳 will give you -405掳, yet another equivalent.
  • This illustrates how angles can continue indefinitely in either direction, wrapped around their cyclical nature.
Understanding both negative and positive angles ensures flexibility in representing any angle on the circle with various coterminal angles.

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

Sketching the Graph of a Trigonometric Function In Exercises \(55-66,\) sketch the graph of the function. $$y=-\sin \frac{2 \pi x}{3}$$

Think About It How do the ranges of the cosine function and the secant function compare?

Finding Composite Functions In Exercises \(63-66,\) find the composite functions \(f^{\circ} g\) and \(g \circ f\) . Find the domain of each composite function. Are the two composite functions equal? $$\begin{array}{l}{f(x)=\frac{1}{x}} \\ {g(x)=\sqrt{x+2}}\end{array}$$

Combinations of Functions In Exercises 59 and 60, find (a) \(f(x)+g(x),\) (b) \(f(x)-g(x)\)(c) \(f(x) \cdot g(x),\) and (d) \(f(x) / g(x)\) $$\begin{array}{l}{f(x)=x^{2}+5 x+4} \\ {g(x)=x+1}\end{array}$$

Deciding Whether an Equation Is a Function In Exercises \(43-46,\) determine whether \(y\) is a function of \(x .\) $$ x^{2}+y^{2}=16 $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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.