/*! 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 19 Find the approximate value of ea... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 19

Find the approximate value of each expression to the nearest tenth. $$ \sec (4.71) $$

Short Answer

Expert verified
41.5

Step by step solution

01

- Understand the problem

The task is to find the tangent (tan) of the angle 1.56 radians and approximate it to the nearest tenth.
02

- Use a calculator

Enter the value 1.56 into a scientific calculator and use the tangent function to find the result.
03

- Obtain the result

By inputting 1.56 into the calculator and pressing the tan button, we get approximately 41.526367.
04

- Round to the nearest tenth

To round to the nearest tenth, we look at the first digit after the decimal point. Here, 41.526367 rounded to the nearest tenth is 41.5.

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Key Concepts

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

tan function
The tangent function, often abbreviated as tan, is one of the basic trigonometric functions in mathematics. It relates to the angles in right triangles. Specifically, for an angle in a right triangle, the tangent is the ratio of the length of the opposite side to the adjacent side. Mathematically, it can be given by the formula: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \).
In our problem, we are dealing with radian measure, where 1.56 is the angle. The approximate value of an angle in radians can be found using scientific calculators, which have built-in trigonometric functions.
scientific calculator
A scientific calculator is a powerful tool that can perform many mathematical functions, including trigonometric operations like finding the tangent of an angle. To find \( \tan(1.56) \) using a scientific calculator, follow these steps:
  • Turn on the calculator.
  • Ensure it is set to radian mode (if necessary, switch from degrees to radians).
  • Enter the angle value 1.56.
  • Press the tan button.
  • Read the result displayed on the calculator screen, which for this case is approximately 41.526367.
Scientific calculators ensure precise calculations, saving time and reducing errors in the process of finding trigonometric values.
rounding decimals
Rounding decimals is an essential mathematical skill used to simplify numbers while maintaining a value close to the original. To round to the nearest tenth, follow these steps:
  • Identify the tenths place: the first digit after the decimal point.
  • Look at the next digit (hundredths place).
  • If the hundredths place digit is 5 or more, increase the tenths place digit by one.
  • If the hundredths place digit is less than 5, keep the tenths place digit the same.
In our example, 41.526367 rounded to the nearest tenth involves:
The tenths place is 5 and the hundredths place is 2. Since 2 is less than 5, the tenths place remains 5. Therefore, 41.526367 rounded to the nearest tenth is 41.5.
By mastering rounding, you can ensure your answers are practical and easier to interpret.

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Most popular questions from this chapter

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WRITING/DISCUSSION Even or Odd An even function is one for which \(f(-x)=f(x)\) and an odd function is one for which \(f(-x)=-f(x)\). Determine whether \(f(x)=\sin (x)\) and \(f(x)=\cos (x)\) are even or odd functions and explain your answers.
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