/*! 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 37 In Problems \(33-40,\) convert t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 37

In Problems \(33-40,\) convert the given angle from radians to degrees. $$ 5 \pi $$

Short Answer

Expert verified
The angle \(5\pi\) radians is equal to 900 degrees.

Step by step solution

01

Understand the Problem

We need to convert an angle from radians to degrees. The given angle is \(5\pi\) radians.
02

Recall the Conversion Formula

To convert radians to degrees, use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180}{\pi} \).
03

Plug in the Radian Measure

Substitute \(5\pi\) for the radian measure in the conversion formula: \( \text{Degrees} = 5\pi \times \frac{180}{\pi} \).
04

Simplify the Expression

Cancel \(\pi\) in the numerator and the denominator: \( \text{Degrees} = 5 \times 180 \).
05

Calculate the Result

Multiply \(5\) by \(180\) to get the degree measure: \( \text{Degrees} = 900 \).

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.

Radians to Degrees
The angle measurement can be quite tricky when you consider different systems, like radians and degrees. Each system has its own way of expressing angles, and one vital task is converting between them.

Radian measures are often used in mathematics due to their natural connection with the radius of a circle. Meanwhile, degrees are more common in everyday contexts.
  • There are approximately 57.3 degrees in one radian.
  • Picturing this visually, a radian is the angle created when one radius length is laid along the circumference of a circle.
  • Degrees divide a circle into 360 parts, making it a more intuitive system for many people.
Understanding how to make these conversions allows seamless calculations and a better grasp of mathematical problems.
Conversion Formula
To convert an angle from radians to degrees, you use a specific formula that revolves around the relationship between these two units.

The formula is:\[\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\]This equation works because:
  • A complete circle is 360 degrees, which corresponds to \(2\pi\) radians.
  • Therefore, there are \(\frac{180}{\pi}\) degrees per radian.
By plugging the radian value into this formula, it seamlessly converts the angle measurement into degrees. This conversion is foundational and simplifies many complex mathematical problems, especially those involving trigonometry.
Multiplication in Conversion
Once you have the conversion formula ready, it's time to perform the actual calculation using multiplication.

For instance, if you have a value like \(5\pi\) radians and wish to convert it into degrees, here's what you do:
  • Insert the radian value into the formula: \(5\pi \times \frac{180}{\pi}\).
  • Notice that \(\pi\) in the numerator and denominator cancel out.
  • This leaves you with \(5 \times 180\) degrees.
  • Finally, perform the multiplication: \(5 \times 180 = 900\) degrees.
Conducting this process involves straightforward arithmetic, but it's crucial to carefully maintain accuracy during each step. Multiplication in conversion ensures you arrive at the precise degree measurement that corresponds to the original radian value.

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

If \(3 \cos x=\sin x\), find all values of \(\tan x, \cot x\) \(\sec x,\) and \(\csc x\)

Find the indicated value without the use of a calculator. $$ \sec 7 \pi $$

Find the amplitude, period, and phase shift of the given function. Sketch at least one cycle of the graph. $$ y=2 \cos \left(-2 \pi x-\frac{4 \pi}{3}\right) $$

Describe in words how you would obtain the graph of the given function by starting with the graph of \(y=\sin x\) (Problem 65 ) and the graph of \(y=\cos x(\) Problem 66\()\). $$ y=5+3 \sin (2 x-\pi) $$

Write an equation of the function whose graph is described in words. The graph of \(y=\cos x\) is vertically stretched up by a factor of 3 and shifted down by 5 units. One cycle of \(y=\cos x\) on \([0,2 \pi]\) is compressed to [0 \(\pi / 3]\) and then the compressed cycle is shifted horizontally \(\pi / 4\) units to the left.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.