/*! 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 93 Find the function value. Round t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 93

Find the function value. Round to four decimal places. $$\cos 5417^{\circ}$$

Short Answer

Expert verified
The value of \(\cos 5417掳\) is approximately \(0.7986\).

Step by step solution

01

Convert degrees to a standard range

Simplify the angle by reducing it to an equivalent angle between 0掳 and 360掳. Do this by finding the remainder when 5417掳 is divided by 360掳: \(5417 \div 360 = 15\) R \(37\). Thus, \(5417掳 = 37掳\) (since \(5417 = 15 \times 360 + 37\)).
02

Calculate the cosine of the reduced angle

Now find the cosine of the simplified angle, \(37掳\). Use a calculator to find that: \(\cos 37掳 \approx 0.7986\) (rounded to four decimal places).

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!

Key Concepts

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

Angle Simplification
When working with trigonometric functions involving large angles, angle simplification is essential.
This process helps in converting any angle to a basic equivalent that lies within the standard range of 0掳 to 360掳.
Here's why this is useful:
  • Trigonometric functions like cosine repeat their values in cycles every 360掳.
  • Reducing the angle makes calculations much simpler and more manageable.
In practice, simplifying an angle means finding the remainder when the given angle is divided by 360掳. So in the problem given, we calculate:
\( 5417掳 \div 360 \approx 15 \times 360 + 37掳 \)
That remainder, 37掳, is the simplified angle.
Degree Conversion
Degree conversion is the process of changing the angle measure to make it fit into a manageable range.
In trigonometric functions, this often involves reducing the angle to a standard range from 0掳 to 360掳.
Why is this important?
  • Operations become easier to compute.
  • Understanding angle behavior within a single 360掳 cycle becomes straightforward.
For our angle, 5417掳, converting it involves division and finding the remainder:
\( 5417掳 \div 360 = 15 \) remainder \( 37掳 \). This means that 5417掳 is equivalent to 37掳 as far as the cosine function is concerned.
Cosine Calculation
Cosine calculation is the step where the trigonometric function value is actually determined.
Having simplified the angle to within 0掳 to 360掳, we can now easily calculate the cosine.
For the angle 37掳, use a calculator to determine:
\[ \cos 37掳 \approx 0.7986 \]
Round this to four decimal places.
Here are some key points to note:
  • Most scientific calculators have a 'cos' function for direct calculation.
  • Ensure your calculator is set to degree mode for this operation.
So, the cosine of 5417掳 simplifies to the cosine of 37掳, which equals approximately 0.7986.

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

Make a hand-drawn graph of the function. Then check your work using a graphing calculator. $$f(x)=2^{-x}$$

Find the maximum and minimum values of the function. $$y=2 \cos \left|3\left(x-\frac{\pi}{2}\right)\right|+6$$

Find the function value. Round to four decimal places. $$\cos 205.5^{\circ}$$

$$\text {Graph each of the following.}$$ $$f(x)=e^{-0.4 x} \sin x$$

Find the reference angle and the exact function value if they exist. $$\tan 0^{\circ}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.