/*! 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 31 Determine the quadrant in which ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 31

Determine the quadrant in which each angle lies. (a) \(130^{\circ}\) (b) \(285^{\circ}\)

Short Answer

Expert verified
The angle \(130^{\circ}\) is in Quadrant 2 while the angle \(285^{\circ}\) is in Quadrant 4.

Step by step solution

01

Identify the quadrant for angle one

The first angle is \(130^{\circ}\). Since this value is smaller than \(180^{\circ}\) but greater than \(90^{\circ}\), we can conclude that the angle lies in Quadrant 2.
02

Identify the quadrant for angle two

The second angle is \(285^{\circ}\). This value is greater than \(180^{\circ}\) but lesser than \(360^{\circ}\), so we can affirm that the angle is located in Quadrant 4.

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.

Quadrant Identification
Identifying the quadrant in which an angle lies is all about understanding the coordinate plane and how angles are positioned within it. The 2D coordinate plane is divided into four parts, known as quadrants. These quadrants are numbered counterclockwise starting from the positive x-axis. Here鈥檚 a simple breakdown:
  • 1st Quadrant: Angles between \(0^{\circ}\) and \(90^{\circ}\)
  • 2nd Quadrant: Angles between \(90^{\circ}\) and \(180^{\circ}\)
  • 3rd Quadrant: Angles between \(180^{\circ}\) and \(270^{\circ}\)
  • 4th Quadrant: Angles between \(270^{\circ}\) and \(360^{\circ}\)
To determine which quadrant an angle lies in, check the degree measure of the angle and compare it against these ranges. This method is straightforward and always helps in quickly identifying the angle鈥檚 quadrant.
Degree Measure
The degree measure is a way of expressing the size of an angle in degrees. This is fundamental when working with angles on the coordinate plane. One full rotation around a circle equals \(360^{\circ}\). So, angles are measured from \(0^{\circ}\) to \(360^{\circ}\).

Degrees provide a standardized way to measure and compare angles. Knowing the degree measure helps in determining the quadrant the angle lies in and also in performing calculations or transformations of angles. Keep in mind:
  • An angle can be small, large, or even a part of a full circle.
  • Understanding degrees is crucial for applications in trigonometry, physics, and even in fields like engineering.
Get comfortable with reading and calculating degree measures, as this will aid significantly in working with angles in any math problem.
Angle Positioning
Positioning an angle on a coordinate plane involves understanding how the angle starts at the positive x-axis and rotates counterclockwise. Consider the four quadrants and visualize where the angle will terminate after being measured from \(0^{\circ}\).

Visualizing angles:
  • Start from the positive x-axis for \(0^{\circ}\).
  • Proceed counterclockwise to measure the angle.
  • The position of the angle's terminal side will tell you the quadrant.
The way angles are positioned not only helps to identify the quadrant but also connects to concepts in trigonometry, where sine and cosine values differ based on the quadrant. Understanding this positioning allows you to see the relationships between different angles and predict their properties in relation to the axes.

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

In Exercises 83-88, use a graphing utility to graph the function. $$ f(x)=-3+\arctan (\pi x) $$

Write an algebraic expression that is equivalent to the expression. $$ \sec [\arcsin (x-1)] $$

In Exercises 19-34, use a calculator to evaluate the expression. Round your result to two decimal places. $$ \arcsin 0.45 $$

Describe the behavior of \(f(\theta)=\sec \theta\) at the zeros of \(g(\theta)=\cos \theta\). Explain your reasoning.

Define the inverse secant function by restricting the domain of the secant function to the intervals \([0, \pi / 2)\) and \((\pi / 2, \pi]\), and sketch its graph.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.