How do I write radian decimals in terms of Pi?

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In summary, to convert degrees to radians, multiply the degree measure by π/180 or divide by 180 and then multiply by π. To write a decimal in terms of pi, divide the decimal by π and multiply by 180. This can also be used to convert radians to degrees. Yes, you can write a radian decimal in terms of pi as a fraction by dividing the decimal by π and simplifying the resulting fraction. There is a specific formula for writing radian decimals in terms of pi, which is πradians = 180 degrees and can be used for conversions.
  • #1
jester0608
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How would i write 1.047 rad in terms of pi? I know the answer i will get is Pi/3 rad, but HOW do i get this answer? I know how to convert degrees to radians and vice versa in terms of pi but this particular question is in radians. Help?
 
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  • #2
1.047/pi≈1/3
1/3*pi=pi/3
 
  • #3
n_kelthuzad said:
1.047/pi≈1/3
1/3*pi=pi/3

But when I calculate 1.047 / pi I get 0.33327. How did you get 1.047/pi ≈ 1/3 ? that's the only part i don't understand
 
  • #4
Since your result 1.047 is written with 4 significant figures, you ought to keep that many in [itex]\theta = \pi / x \Rightarrow x =\pi / \theta = 3.001[/itex].
 
  • #5


To write a radian decimal in terms of pi, you can use the formula: radians = degrees * (pi/180). In this case, 1.047 radians would be written as 1.047 * (pi/180) = (1.047 * pi)/180. Simplifying this further, we get (pi/3)/180 = pi/540. Therefore, 1.047 radians can be written as pi/540 in terms of pi.

To understand how we arrived at this answer, we can break it down into steps:

Step 1: Convert 1.047 radians to degrees by multiplying it by 180/pi. This gives us 1.047 * (180/pi) = 59.964 degrees.

Step 2: Now, we can use the formula to convert degrees to radians in terms of pi: radians = degrees * (pi/180). Plugging in the value of 59.964 degrees, we get radians = 59.964 * (pi/180).

Step 3: Simplifying this further, we get (pi/3)/180 = pi/540. Therefore, 1.047 radians can be written as pi/540 in terms of pi.

I hope this helps clarify the process of writing radian decimals in terms of pi. Remember to always use the formula and convert to degrees first before converting to radians in terms of pi.
 

1. How do I convert degrees to radians?

To convert degrees to radians, multiply the degree measure by π/180 or simply divide by 180 and then multiply by π.

2. How do I write a decimal in terms of pi?

To write a decimal in terms of pi, divide the decimal by π and multiply by 180. For example, to write 0.5 in terms of pi, divide 0.5 by π and multiply by 180. The result would be 90π.

3. Can I write a radian decimal in terms of pi as a fraction?

Yes, you can write a radian decimal in terms of pi as a fraction. For example, 0.75 radians can be written as 3π/4. Simply divide the decimal by π and simplify the resulting fraction.

4. How do I convert a radian decimal to degrees?

To convert a radian decimal to degrees, multiply the radian measure by 180/π or simply divide by π and then multiply by 180.

5. Is there a specific formula for writing radian decimals in terms of pi?

Yes, the formula for writing radian decimals in terms of pi is: πradians = 180 degrees. This formula can be used to convert between radians and degrees and vice versa.

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