/*! 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 27 Determine whether the angles in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 27

Determine whether the angles in each given pair are coterminal. $$ 22^{\circ},-1058^{\circ} $$

Short Answer

Expert verified
The angles 22掳 and -1058掳 are coterminal because -1058掳 is equivalent to 22掳 after adding multiples of 360掳.

Step by step solution

01

Understand Coterminal Angles

Two angles are coterminal if they differ by a multiple of 360 degrees. This means that when you add or subtract 360 degrees enough times, one angle should equal the other.
02

Calculate the Equivalent Positive Angle for -1058掳

To find an angle coterminal with ewlineeangle -1058掳, we keep adding 360掳 until the result is between 0掳 and 360掳.ewline Start with: $$ -1058掳 + 360掳 = -698掳 $$ewlineeangle -698掳 + 360掳 = -338掳 ewlineeangle -338掳 + 360掳 = 22掳So -1058掳 is coterminal with 22掳.
03

Compare with the Given Angle

Since the equivalent positive angle we found for -1058掳 is 22掳, and it matches the given angle 22掳, these two angles are coterminal.

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.

Coterminal Angles
Coterminal angles are angles that share the same terminal side when drawn in standard position. Imagine starting from the positive x-axis and rotating around the circle. If two angles land on the same final line, they are coterminal. For example, an angle of 30掳 and an angle of 390掳 are coterminal because 390掳 is just one full rotation (360掳) plus 30掳. This concept is essential for various fields including trigonometry, physics, and engineering because it simplifies complex angle measures.

To find coterminal angles, you can either add or subtract 360掳 (a full circle) any number of times. For instance:
  • Adding 360掳: \[ 45掳 + 360掳 = 405掳 \]
  • Subtracting 360掳: \[ 45掳 - 360掳 = -315掳 \]

Both 405掳 and -315掳 are coterminal with 45掳.
Angle Equivalency
Angle equivalency is a crucial idea behind coterminal angles. Two angles are equivalent if they differ by a multiple of 360掳. This is because 360掳 represents a full rotation around a circle, bringing the angle back to its starting point. Think of angle equivalency as drawing the same angle over and over, but indicating more or fewer rotations.

For example, to determine if 22掳 and -1058掳 are coterminal, you can follow these steps:
  • Keep adding or subtracting 360掳 to the negative angle until the result is between 0掳 and 360掳.
  • \[ -1058掳 + 360掳 = -698掳 \] \[ -698掳 + 360掳 = -338掳 \] \[ -338掳 + 360掳 = 22掳 \]

Since the calculation shows that -1058掳 eventually equals 22掳, they are equivalent, meaning they are coterminal.
Angle Calculation
Calculating coterminal angles involves a few straightforward steps. Sometimes angles are given in large positive or negative numbers, and converting them can make understanding them much easier.

Here's a step-by-step method to find coterminal angles:
  • Start with the given angle. If it's negative or greater than 360掳, you'll need to adjust it.
  • Add or subtract 360掳 until the angle falls within the range of 0掳 to 360掳.

In the case of the problem given:

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

Find the exact area of the sector of the circle with the given radius and central angle. $$ r=12, \alpha=\pi / 3 $$

Use a calculator to evaluate each expression. Round approximate answers to four decimal places. $$ \frac{\sin (9.2)}{\cos (9.2)} $$

Use a calculator to find the value of each function. Round answers to four decimal places. $$ \sec \left(-9^{\circ} 4^{\prime} 7^{\prime \prime}\right) $$

Solve each problem. If \(\tan \alpha=1 / 70,\) then what is \(\cot \alpha ?\)

Find the exact value of each expression for the given value of \(\theta\) Do not use a calculator. $$ \sin (\theta / 2) \text { if } \theta=2 \pi / 3 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.