/*! 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 105 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 105

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used a half-angle formula to find the exact value of \(\cos 100^{\circ}\)

Short Answer

Expert verified
The statement doesn't make sense because half-angle identities are typically used to find exact values for half of known angles, and 100 degrees is not half of any common angles.

Step by step solution

01

Understanding the Statement

The statement says that a half-angle formula was used to find the exact value of \(\cos 100^{\circ}\). It needs to be determined if this approach makes sense or not.
02

Recalling Half-Angle Formulas

Recall the half-angle identity for cosine, \(\cos \frac{\theta}{2} = \pm \sqrt{\frac{1 + \cos \theta}{2}}.\) This identity allows for the exact calculation of the half angles of known angles.
03

Analyzing the Statement

\(\cos 100^{\circ}\) is not a half-angle of any commonly known angles (30, 45, 60, 90,180). Hence, we may say that it is not reasonable to use the half-angle formula to find \(\cos 100^{\circ}\) exactly, since we will not have a simple form for \(2 \times 100 = 200^{\circ}\), outside the standard unit circle angles. We could technically use the half-angle formula, but it wouldn't simplify the process.

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

Solve each equation on the interval \([0,2 \pi)\) Do not use a calculator. $$ 2 \cos x-1+3 \sec x=0 $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(\tan x=\frac{\pi}{2}\) has no solution.

Will help you prepare for the material covered in the next section. In each exercise, use exact values of trigonometric functions to show that the statement is true. Notice that each statement expresses the product of sines and/or cosines as a sum or a difference. $$ \cos \frac{\pi}{2} \cos \frac{\pi}{3}=\frac{1}{2}\left[\cos \left(\frac{\pi}{2}-\frac{\pi}{3}\right)+\cos \left(\frac{\pi}{2}+\frac{\pi}{3}\right)\right] $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Using sum and difference formulas, I can find exact values for sine, cosine, and tangent at any angle.

Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$ 5 \sec ^{2} x-10=0 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

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.