675 Degrees to Radians Fraction: An In-Depth Guide to Conversion

Introduction

In mathematics, degrees and radians are two commonly used units for measuring angles. Degrees are based on the concept of a circle divided into 360 equal parts, while radians are based on the concept of the radius of a circle. Converting between degrees and radians is essential for solving various mathematical problems. In this article, we will focus on converting 675 degrees to radians.

Degrees and Radians

Degrees (°)

• A degree is a unit of measurement for angles.
• A full circle is divided into 360 degrees.
• Each degree is further divided into 60 minutes (').
• Each minute is further divided into 60 seconds (").

Radians (rad)

• A radian is a unit of measurement for angles.
• One radian is defined as the angle subtended by an arc length equal to the radius of a circle.
• A full circle contains 2π radians.

Converting 675 Degrees to Radians

To convert 675 degrees to radians, we need to multiply the degree measure by π/180. The formula for conversion is:

radians = degrees × π/180

Plugging in the value of 675 degrees, we get:

radians = 675 × π/180

radians ≈ 11.781

Therefore, 675 degrees is approximately equal to 11.781 radians.

Applications of Converting Degrees to Radians

Converting between degrees and radians has several applications in mathematics, physics, and engineering. Some of the common applications include:

• Trigonometric calculations: Radians are the preferred unit for trigonometric calculations because they simplify the formulas and make them easier to solve.
• Calculus: Calculus involves studying rates of change, and radians are used to measure the rate of change of angles.
• Physics: Radians are used in physics to describe circular motion and other rotational quantities.
• Engineering: Radians are used in engineering to design and analyze structures, machines, and other systems involving circular motion.

Table 1: Degrees to Radians Conversion Table

Table 2: Radians to Degrees Conversion Table

Step-by-Step Approach to Converting Degrees to Radians

1. Multiply the degree measure by π/180.
2. Round the result to the desired number of decimal places. For example, to convert 675 degrees to radians to two decimal places, multiply by 3.14/180 and round to two decimal places:

radians = 675 × 3.14/180

radians ≈ 11.78

Frequently Asked Questions (FAQs)

1. Why is it important to convert degrees to radians?

Radians are the preferred unit for trigonometric calculations and other mathematical operations.

2. Can I use a calculator to convert degrees to radians?

Yes, most calculators have a built-in function for converting degrees to radians.

3. What is the formula for converting radians to degrees?

degrees = radians × 180/π

4. What are some applications of converting degrees to radians?

Trigonometric calculations, calculus, physics, and engineering.

5. How do I convert 45 degrees to radians?

radians = 45 × π/180

radians ≈ 0.785

6. How do I convert π/2 radians to degrees?

degrees = π/2 × 180/π

degrees = 90°

7. What is the difference between degrees and radians?

Degrees are based on the concept of a circle divided into 360 equal parts, while radians are based on the concept of the radius of a circle.

8. Why are radians used in trigonometry?

Radians simplify trigonometric formulas and make them easier to solve.