/*! 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 47 \(\cos (-1.7)\)... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 47

\(\cos (-1.7)\)

Short Answer

Expert verified
The short answer to this problem will be the numerical value obtained from the calculator or software tool for \(\cos(-1.7)\).

Step by step solution

01

Understanding the Problem

Start by understanding that this exercise is about finding the value of cosine for the given angle which is -1.7 radians.
02

Calculating the value of \(\cos(-1.7)\)

In this step, calculate the value of \(\cos(-1.7)\). Use a calculator or a software tool that can calculate trigonometric functions. Make sure the calculator or software is in radian mode, as the problem gives the angle in radians, not degrees.
03

Interpreting the result

The result obtained after the calculation is the value of the \(\cos(-1.7)\) which is positive as per the understanding of the cosine function.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radians
Radians are a unit of angle measurement, distinct from degrees, primarily used in mathematics and engineering. One radian is the angle created when the arc length equals the radius of the circle. To convert between degrees and radians, remember that \( \pi \) radians = 180 degrees. Thus, 1 radian is approximately 57.2958 degrees. This helps when converting angles into a format calculators or software usually require, particularly in trigonometry.

When working with radians:
  • Recognize that angles can be negative, such as \(-1.7\) radians, meaning the angle is measured in the clockwise direction from the positive x-axis.
  • Always ensure your calculator is set to radian mode, especially when dealing with trigonometric functions like sine or cosine.
  • Grasp that radians are often more convenient in calculus and in representations of periodic functions.
Cosine Function
The cosine function is one of the fundamental trigonometric functions. It relates an angle to the ratio of the adjacent side to the hypotenuse in a right triangle. On the unit circle, it represents the x-coordinate of a point.

Important aspects of the cosine function include:
  • The range of cosine values is from \(-1\) to \(1\), meaning any input will yield a result within this interval.
  • It's even, meaning \(\cos(-x) = \cos(x)\), making calculations involving negative angles straightforward.
  • The graph of the cosine function is a wave that repeats every \(2 \pi\) radians, known as its period.
For angles in radians, such as \(-1.7\), understanding these properties makes it easier to calculate or predict behavior without constantly relying on a calculator.
Calculator Usage
When dealing with trigonometric calculations, a calculator is an indispensable tool. However, proper usage is essential to get accurate results. Here are some tips for using a calculator to find values like \( \cos(-1.7) \):

  • First, always ensure your calculator is set to the correct mode. For radians, switch to "Rad" mode rather than "Deg" mode.
  • Input the value exactly as given. For \(-1.7\), make sure to include the negative sign to get the correct result.
  • Familiarize yourself with the specific keys and functions of your calculator model for trigonometric functions.
By following these guidelines, you can avoid common pitfalls like mode errors. Calculators provide precise answers, yet understanding the underlying mathematics clarifies and enriches your learning experience.

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Most popular questions from this chapter

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