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Writing decimal radians in terms of Pi

  1. Feb 20, 2010 #1
    Hello :smile:

    Sorry if this is in the wrong place, I don't know where else to put it.

    Is there a way to write radians as decimals in terms of Pi?

    I'm currently doing Polar Coordinates with Argand Diagrams, and this is something I'm curious about.

    I've just done a question and come out with -0.983 rad. We've left it in decimal form in lectures, but I was just curious to know how I'd go about writing it in terms of Pi.

    [tex]45\deg = 0.785 = \frac{\pi}{4}[/tex]

    [tex]-56.34\deg = -0.983= \frac{?}{?}[/tex]

    Anyone know?

    Also, I've always had trouble with angles. Calculus? Love it. Trig? Huh!

  2. jcsd
  3. Feb 20, 2010 #2
    [tex]-56.34 deg=\frac{-56.34}{180} \pi [/tex]
  4. Feb 20, 2010 #3


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    So, you have an equation with an unknown? Why can't you solve it?
  5. Feb 20, 2010 #4
    Thanks for the replies. :smile:

    I'd never thought of doing that. I'm actually a bit worried now. I should have known that by now.

    Would you happen to know how to convert the -0.983 directly in terms of Pi, without using degrees at any point?

    I'm starting to recognise angles in decimal radians, so I figure it would be good to know (and understand) what they are in terms of Pi.

    I've just got these from further questions:

    [tex]1.047 = \frac{\pi}{3}[/tex]

    [tex]0.707 = \frac{?}{?}[/tex]

    I've seen the second one before, but I can't remember what it is in terms of Pi.

    I'm really sorry, but I don't know what you mean. I can do the questions as I've been shown in lectures. I'm asking about this "conversion" to mostly satisfy my own curiosity. :smile:
  6. Feb 20, 2010 #5
    Assuming you mean "in terms of Pi radians", I guess you're looking for x*Pi = -0.983, which is straightforward algebra. This gives you about -0.313Pi.
  7. Feb 20, 2010 #6
    [tex]0.707 \, \text{rad}=x\, \pi \,rad[/tex]

    Divide both sides by [itex]\pi[/itex] radians:

  8. Feb 20, 2010 #7


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    Hello Matty R! :smile:

    (have a pi: π and a degree: º :wink:)
    You wouldn't! :smile:

    Just leave it in radians …

    why do you think you need to change it? :wink:
  9. Feb 21, 2010 #8


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    Yes, you most likely saw this one from [tex]\frac{1}{\sqrt{2}}[/tex] :smile:
  10. Feb 21, 2010 #9


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    And tiny-tim has a point. You wouldn't change it in terms of [itex]\pi[/itex] because your answer is obviously approximated and most likely since you had to approximate the answer, it's not going to be a nice fractional radian value such as [itex]\pi/4[/itex] etc.
  11. Feb 21, 2010 #10


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    Yes, 0.707 = cos(π/4) = sin(π/4). :wink:
  12. Feb 21, 2010 #11
    Wow. Thanks for all the replies. :smile:

    I think I see where I got a bit confused. I thought everything could be written in terms of Pi, but its the fractions like [tex]\frac{1}{\sqrt2}[/tex] that I need to be looking at.

    I am so bad with angles. Getting better though. :smile:

    I love this site.

    Thank you all very much. :smile:
  13. Feb 21, 2010 #12
    Anything can be written in terms of [itex]\pi[/itex], if you like:

    [tex]\frac{1}{\sqrt{2}}\,\text{rad}=\frac{1}{\sqrt{2}} \cdot \frac{\pi}{\pi}\,\text{rad}\approx 0.225 \pi \, \text{rad} \approx 0.707 \, \text{rad}[/tex]

    Whether you want to just depends on what's most useful or convenient or meaningful, or what kind of answer gives most insight.
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