Converting Between Degrees and Radians

Oct 13, 2025 by miodeya.com 55 views

When dealing with angles in mathematics, it's essential to understand the correct order from least to greatest. Angles can be measured in both degrees and radians, and converting between these units is crucial for accurate calculations. In this article, we will explore the correct order of angles in radians and degrees, and provide examples to illustrate the concept.

Converting Between Degrees and Radians

Before we dive into the correct order of angles, let's briefly review the conversion between degrees and radians. The formula to convert degrees to radians is:

Radians = Degrees × (π/180)

On the other hand, the formula to convert radians to degrees is:

Degrees = Radians × (180/π)

The Correct Order of Angles

Now that we have a basic understanding of converting between degrees and radians, let's examine the given options:

Option A: $255^{\circ}, \frac{2 \pi}{3}, \frac{\pi}{2}, 60^{\circ}, \frac{3 \pi}{10}$

To determine the correct order, we need to convert all angles to a common unit. Let's convert the angles in radians to degrees:

$\frac{2 \pi}{3} = 120^{\circ}$
$\frac{\pi}{2} = 90^{\circ}$
$\frac{3 \pi}{10} = 57^{\circ}$

Now that we have all angles in degrees, we can compare them:

$60^{\circ}$
$57^{\circ}$
$90^{\circ}$
$120^{\circ}$
$255^{\circ}$

The correct order from least to greatest is:

$57^{\circ}$
$60^{\circ}$
$90^{\circ}$
$120^{\circ}$
$255^{\circ}$

Option B: $\frac{3 \pi}{10}, \frac{\pi}{2}, \frac{2 \pi}{3}, 60^{\circ}, 255^{\circ}$

Let's convert the angles in radians to degrees:

$\frac{3 \pi}{10} = 57^{\circ}$
$\frac{\pi}{2} = 90^{\circ}$
$\frac{2 \pi}{3} = 120^{\circ}$

Now that we have all angles in degrees, we can compare them:

$57^{\circ}$
$60^{\circ}$
$90^{\circ}$
$120^{\circ}$
$255^{\circ}$

The correct order from least to greatest is:

$57^{\circ}$
$60^{\circ}$
$90^{\circ}$
$120^{\circ}$
$255^{\circ}$

Option C

Option C is not provided, so we will not consider it in our analysis.

Conclusion

In conclusion, the correct order of angles from least to greatest is:

$57^{\circ}$
$60^{\circ}$
$90^{\circ}$
$120^{\circ}$
$255^{\circ}$

In our previous article, we explored the correct order of angles in radians and degrees. However, we understand that there may be more questions and concerns about this topic. In this article, we will address some frequently asked questions (FAQs) about angles in radians and degrees.

Q: What is the difference between radians and degrees?

A: Radians and degrees are two different units of measurement for angles. Radians are a more natural unit for mathematical calculations, while degrees are more commonly used in everyday applications.

Q: How do I convert degrees to radians?

A: To convert degrees to radians, you can use the formula:

Radians = Degrees × (π/180)

Q: How do I convert radians to degrees?

A: To convert radians to degrees, you can use the formula:

Degrees = Radians × (180/π)

Q: What is the relationship between radians and degrees?

A: The relationship between radians and degrees is based on the fact that a full circle is equal to 2π radians or 360 degrees. This means that:

1 radian = (180/π) degrees
1 degree = (π/180) radians

Q: How do I determine the correct order of angles?

A: To determine the correct order of angles, you need to convert all angles to a common unit. If you are working with angles in radians, you can convert them to degrees using the formula:

Degrees = Radians × (180/π)

If you are working with angles in degrees, you can convert them to radians using the formula:

Radians = Degrees × (π/180)

Once you have all angles in the same unit, you can compare them to determine the correct order.

Q: What are some common angles in radians and degrees?

A: Some common angles in radians and degrees include:

π/2 radians = 90 degrees
π radians = 180 degrees
2π radians = 360 degrees
π/3 radians = 60 degrees
π/4 radians = 45 degrees

Q: How do I use angles in real-world applications?

A: Angles are used in a wide range of real-world applications, including:

Navigation: Angles are used to determine direction and location.
Engineering: Angles are used to design and build structures, such as bridges and buildings.
Physics: Angles are used to describe the motion of objects and the forces acting upon them.
Computer Science: Angles are used in computer graphics and game development to create 3D models and animations.

Conclusion

In conclusion, angles in radians and degrees are an essential part of mathematics and are used in a wide range of real-world applications. By understanding the correct order of angles and how to convert between radians and degrees, you can apply this knowledge to solve problems and make informed decisions.