Writing decimal radians in terms of Pi

1. Feb 20, 2010

Matty R

Hello

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.

$$45\deg = 0.785 = \frac{\pi}{4}$$

$$-56.34\deg = -0.983= \frac{?}{?}$$

Anyone know?

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

Thanks

2. Feb 20, 2010

elibj123

$$-56.34 deg=\frac{-56.34}{180} \pi$$

3. Feb 20, 2010

Hurkyl

Staff Emeritus
So, you have an equation with an unknown? Why can't you solve it?

4. Feb 20, 2010

Matty R

Thanks for the replies.

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:

$$1.047 = \frac{\pi}{3}$$

$$0.707 = \frac{?}{?}$$

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.

5. Feb 20, 2010

slider142

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.

6. Feb 20, 2010

Rasalhague

$$0.707 \, \text{rad}=x\, \pi \,rad$$

Divide both sides by $\pi$ radians:

$$\frac{0.707}{\pi}=x$$

7. Feb 20, 2010

tiny-tim

Hello Matty R!

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

Just leave it in radians …

why do you think you need to change it?

8. Feb 21, 2010

Mentallic

Yes, you most likely saw this one from $$\frac{1}{\sqrt{2}}$$

9. Feb 21, 2010

Mentallic

And tiny-tim has a point. You wouldn't change it in terms of $\pi$ 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 $\pi/4$ etc.

10. Feb 21, 2010

tiny-tim

Yes, 0.707 = cos(π/4) = sin(π/4).

11. Feb 21, 2010

Matty R

Wow. Thanks for all the replies.

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 $$\frac{1}{\sqrt2}$$ that I need to be looking at.

I am so bad with angles. Getting better though.

I love this site.

Thank you all very much.

12. Feb 21, 2010

Rasalhague

Anything can be written in terms of $\pi$, if you like:

$$\frac{1}{\sqrt{2}}\,\text{rad}=\frac{1}{\sqrt{2}} \cdot \frac{\pi}{\pi}\,\text{rad}\approx 0.225 \pi \, \text{rad} \approx 0.707 \, \text{rad}$$

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