/*! 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 64 Find a positive angle less than ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 64

Find a positive angle less than \(360^{\circ}\) or \(2 \pi\) that is coterminal with the given angle. $$\frac{17 \pi}{5}$$

Short Answer

Expert verified
The positive angle less than \(2\pi\) which is coterminal with \(\frac{17\pi}{5}\) is \(\frac{2\pi}{5}\) radians.

Step by step solution

01

Given angle in radians

We are given the angle \( \frac{17\pi}{5}\) in radians.
02

Identifying the coterminal angle

We understand that angles are coterminal if they end up at the same position on the circle when starting from the origin. We can achieve this by adding or subtracting multiples of complete rotations, which is \(2\pi\) radians or \(360^\circ\). So, to find a positive coterminal angle less than \(2\pi\), subtract multiples of \(2\pi\) until the resultant angle falls within the range of 0 and \(2\pi\).
03

Subtract multiples of \(2 \pi\)

Subtract multiples of \(2\pi\) from the given angle \(\frac{17\pi}{5}\) until we get a value less than \(2\pi\). The largest multiple of \(2\pi\) that is less than \(\frac{17\pi}{5}\) is \(2*3\pi = 6\pi\). Hence, perform the subtraction: \(\frac{17\pi}{5} - 6\pi = \frac{2\pi}{5}\).
04

The coterminal angle is

So the positive angle less than \(2\pi\) that is coterminal with \(\frac{17\pi}{5}\) is \(\frac{2\pi}{5}\) radians.

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!

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

Use a graphing utility to graph each pair of functions in the same viewing rectangle. Use a viewing rectangle that shows the graphs for at least two periods. $$y=-3.5 \cos \left(\pi x-\frac{\pi}{6}\right) \text { and } y=-3.5 \sec \left(\pi x-\frac{\pi}{6}\right)$$

Find all zeros of \(f(x)=2 x^{3}-5 x^{2}+x+2\) (Section \(2.5, \text { Example } 3)\)

Describe a relationship between the graphs of \(y=\sin x\) and \(y=\cos x\)

Graph \(f, g,\) and \(h\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi .\) Obtain the graph of h by adding or subtracting the corresponding \(y\) -coordinates on the graphs of \(f\) and \(g\) $$f(x)=\sin x, g(x)=\cos 2 x, h(x)=(f-g)(x)$$

Use a vertical shift to graph one period of the function. $$y=-3 \cos 2 \pi x+2$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.