Converting Degrees to Radians: A Quick Guide

In summary, to convert degrees to radians, you can use the formula: radians = degrees * (π/180). The difference between degrees and radians is that degrees are commonly used in everyday life while radians are used more frequently in mathematics and science. Yes, you can convert radians to degrees using the formula: degrees = radians * (180/π). Radians are used in mathematics because they are a more natural unit for measuring angles. To quickly convert from degrees to radians, simply divide the number of degrees by 180 and multiply by π.
  • #1
CrossFit415
160
0
I know that 65° = pi/180 = 13pi / 36. But when I divide 65 / 180° I get. 3261. How would I convert this into 13pi/36 ? I know I am forgetting the basics..
 
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  • #2
[tex]2\pi = 360^{\circ}[/tex]
 
  • #3
Do I multiplty 65° into 2pi?
 
  • #4
Reduce the fraction, of course! 65 and 180 have 5 as a common factor.

[tex]65^{\circ} = \frac{65 \pi}{180} = \frac{65 \pi \div 5}{180 \div 5} = \frac{13 \pi}{36}[/tex]
 
  • #5
Lol thanks! I was just having a dull moment. :)
 

Related to Converting Degrees to Radians: A Quick Guide

1. How do I convert degrees to radians?

To convert degrees to radians, you can use the formula: radians = degrees * (π/180). This formula is based on the fact that there are 2π radians in a full circle (360 degrees).

2. What is the difference between degrees and radians?

Degrees and radians are both units of measurement for angles. Degrees are commonly used in everyday life, while radians are used more frequently in mathematics and science. One full circle is equal to 360 degrees or 2π radians. Radians are considered to be a more natural unit for measuring angles in mathematical calculations.

3. Can I convert radians to degrees?

Yes, you can convert radians to degrees using the formula: degrees = radians * (180/π). This formula is the inverse of the formula used to convert degrees to radians.

4. Why do we use radians instead of degrees in mathematics?

Radians are used in mathematics because they are a more natural unit for measuring angles. Radians are based on the radius of a circle and the length of the arc subtended by an angle, making them easier to work with in mathematical calculations and equations.

5. How do I convert from degrees to radians quickly?

If you need to quickly convert from degrees to radians, you can use the fact that 180 degrees is equal to π radians. So, to convert from degrees to radians, simply divide the number of degrees by 180 and multiply by π.

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