# 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.