/*! 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 22 Find the exact value of the trig... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 22

Find the exact value of the trigonometric function. If the value is undefined, so state. $$\sin \left(-\frac{5 \pi}{3}\right)$$

Short Answer

Expert verified
The exact value of \(\sin(-5\pi/3)\) is \( \sqrt{3}/2 \).

Step by step solution

01

Recognize the periodic property of sine function

The sine function is periodic with a period of \(2\pi\). In other words, \(\sin(-5\pi/3)\) is the same as \(\sin(\pi/3)\) because these two angles differ by an integer multiple of the period.
02

Use definition of negative angles in trigonometry

The value of the sine function at a negative angle is equal to the negation of its value at the corresponding positive angle. So, \(\sin(-\theta) = -\sin(\theta)\). However, in this case, since we have \(\sin(-5\pi/3)\), we notice that the angle \(-5\pi/3 + 2\pi = \pi/3\) is a positive angle between 0 and \(2\pi\). Therefore, we actually have \(\sin(-5\pi/3) = \sin(\pi/3)\), without the negation.
03

Find the exact value of the function

The exact value of \(\sin(\pi/3)\) or equivalent to \(\sin(60^\circ)\) is well known: it is \( \sqrt{3}/2 \).

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 function. $$y=2+\sec \frac{x}{2}$$

If \(g(x)=x^{2}+2\) and \(h(x)=\cos x,\) find \(g[h(x)]\)

Estimate, to the nearest tenth, \(\cot \frac{\pi}{3} .[4.2]\)

Graph at least one full period of the function defined by each equation. $$y=2 \cos 2 x$$

Write an equation for a cosine function using the given information. Amplitude \(=4.2 ;\) period \(=1\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.