Convert The Given Radian Measure To A Degree Measure. 1.1 Π 1.1 \pi 1.1 Π A. − 99 ∘ -99^{\circ} − 9 9 ∘ B. − 198 ∘ -198^{\circ} − 19 8 ∘ C. 99 ∘ 99^{\circ} 9 9 ∘ D. 198 ∘ 198^{\circ} 19 8 ∘

Understanding the Relationship Between Radians and Degrees

In mathematics, radians and degrees are two units used to measure angles. While radians are the standard unit used in calculus and trigonometry, degrees are more commonly used in everyday applications. To convert between these two units, we need to understand the relationship between them.

The Conversion Formula

The conversion formula between radians and degrees is given by:

degrees = (radians × 180)/π

This formula can be used to convert a radian measure to a degree measure, and vice versa.

Converting $1.1 \pi$ Radians to Degrees

Now, let's apply the conversion formula to convert $1.1 \pi$ radians to degrees.

Step 1: Multiply the radian measure by 180

First, we multiply $1.1 \pi$ by 180 to get:

1.1 × 180 = 198

Step 2: Divide the result by π

Next, we divide the result by π to get:

198/π ≈ 62.83

However, this is not the correct answer. We need to consider the sign of the radian measure.

Step 3: Consider the Sign of the Radian Measure

Since $1.1 \pi$ is greater than $2 \pi$, it represents an angle greater than 360°. To convert this to a degree measure, we need to subtract $2 \pi$ from $1.1 \pi$ and then apply the conversion formula.

1.1 π - 2π = -0.9π

Now, we can apply the conversion formula:

degrees = (-0.9 × 180)/π ≈ -198

Therefore, the correct conversion of $1.1 \pi$ radians to degrees is -198°.

Conclusion

In conclusion, converting a radian measure to a degree measure requires understanding the relationship between radians and degrees and applying the conversion formula. By following the steps outlined above, we can accurately convert $1.1 \pi$ radians to degrees, which is -198°.

Key Takeaways

• The conversion formula between radians and degrees is given by: degrees = (radians × 180)/π
• To convert a radian measure to a degree measure, we need to consider the sign of the radian measure.
• Subtracting $2 \pi$ from the radian measure can help us convert it to a degree measure.

Practice Problems

1. Convert $2.5 \pi$ radians to degrees.
2. Convert $-3 \pi$ radians to degrees.
3. Convert $4 \pi$ radians to degrees.

Answers

1. -540°
2. 540°
3. 720°

Additional Resources

For more practice problems and examples, check out the following resources:

• Khan Academy: Radians and Degrees
• Mathway: Radians to Degrees Converter
• Wolfram Alpha: Radians to Degrees Converter
  Frequently Asked Questions (FAQs) About Converting Radian Measure to Degree Measure =====================================================================================

Q: What is the relationship between radians and degrees?

A: Radians and degrees are two units used to measure angles. While radians are the standard unit used in calculus and trigonometry, degrees are more commonly used in everyday applications.

Q: How do I convert a radian measure to a degree measure?

A: To convert a radian measure to a degree measure, you can use the conversion formula: degrees = (radians × 180)/π.

Q: What if the radian measure is greater than 2π?

A: If the radian measure is greater than 2π, you need to subtract 2π from the radian measure before applying the conversion formula.

Q: What if the radian measure is negative?

A: If the radian measure is negative, you need to consider the sign of the radian measure when applying the conversion formula.

Q: Can I use a calculator to convert a radian measure to a degree measure?

A: Yes, you can use a calculator to convert a radian measure to a degree measure. However, make sure to use the correct conversion formula and consider the sign of the radian measure.

Q: What are some common mistakes to avoid when converting a radian measure to a degree measure?

A: Some common mistakes to avoid when converting a radian measure to a degree measure include:

• Not considering the sign of the radian measure
• Not subtracting 2π from the radian measure when it is greater than 2π
• Not using the correct conversion formula

Q: How do I check my work when converting a radian measure to a degree measure?

A: To check your work when converting a radian measure to a degree measure, you can:

• Use a calculator to verify your answer
• Check your work using a different method, such as converting the radian measure to a decimal degree measure
• Use a conversion chart or table to verify your answer

Q: What are some real-world applications of converting a radian measure to a degree measure?

A: Some real-world applications of converting a radian measure to a degree measure include:

• Navigation: Converting radian measures to degree measures is essential for navigation, as it allows pilots and sailors to accurately measure angles and distances.
• Engineering: Converting radian measures to degree measures is essential for engineering, as it allows engineers to accurately measure angles and distances in the design and construction of buildings and other structures.
• Science: Converting radian measures to degree measures is essential for science, as it allows scientists to accurately measure angles and distances in the study of the natural world.

Q: Can I convert a degree measure to a radian measure?

A: Yes, you can convert a degree measure to a radian measure using the conversion formula: radians = (degrees × π)/180.

Q: What are some common mistakes to avoid when converting a degree measure to a radian measure?

A: Some common mistakes to avoid when converting a degree measure to a radian measure include:

• Not using the correct conversion formula
• Not considering the sign of the degree measure
• Not using a calculator to verify your answer

Q: How do I check my work when converting a degree measure to a radian measure?

A: To check your work when converting a degree measure to a radian measure, you can:

• Use a calculator to verify your answer
• Check your work using a different method, such as converting the degree measure to a decimal radian measure
• Use a conversion chart or table to verify your answer