• Nov 13th 2011, 11:31 AM
David Green

if a question asks for angle measurements in both degrees and radians, then gives typical answers where only two are correct, am I right in thinking that the radian answer would be presented as say example;

1/6 x pie, being the radian answer, whereas 0.5 = 30 degrees.

I know that 1/6 x pie is not the same as 30 degrees just before anyone jumps at me for that statement made!

Thanks

David
• Nov 13th 2011, 11:37 AM
e^(i*pi)
Quote:

Originally Posted by David Green

if a question asks for angle measurements in both degrees and radians, then gives typical answers where only two are correct, am I right in thinking that the radian answer would be presented as say example;

1/6 x pie, being the radian answer, whereas 0.5 = 30 degrees.

I know that 1/6 x pie is not the same as 30 degrees just before anyone jumps at me for that statement made!

Thanks

David

We know from our geometry that $\displaystyle 2\pi = 360^o$

If you divide both sides by 12 you get $\displaystyle \dfrac{\pi}{6} = 30^o$ so pi/6 radians is equal to 30 degrees.

You'd be right in thinking that the radian answer would be represented in term s of pi.
• Nov 13th 2011, 11:58 AM
David Green
How does that stand in an answer to a question then?

I was always lead to believe that each degree equals 60 minutes, so would 1 degree out not be considered significant in an answer?
• Nov 13th 2011, 12:29 PM
Quacky
$\displaystyle \frac{\pi}{6}=30^o$ Why would you be 1 degree out? Just do the conversions carefully and you'll be fine.

$\displaystyle 1$ degree $\displaystyle =\frac{\pi}{180}$ radians.

Knowing the above is all you need to convert between them.

For example, if you measure something as $\displaystyle 54^o$, then this is $\displaystyle 54\times\frac{\pi}{180}^c$

$\displaystyle =\frac{3\pi}{10}^c$

If you have $\displaystyle \frac{\pi}{8}$ radians, this is$\displaystyle \frac{\pi}{8}\times\frac{180}{\pi}^o$
$\displaystyle =22.5^o$

I first encountered radians whilst studying A levels at age 17 in the UK. My examining body, for conversions, only accepted exact conversions between degrees and radians.

Maybe your system is different, I can't say.
• Nov 13th 2011, 01:38 PM
e^(i*pi)
Quote:

Originally Posted by Quacky
I first encountered radians whilst studying A levels at age 17 in the UK. My examining body, for conversions, only accepted exact conversions between degrees and radians.

Maybe your system is different, I can't say.

Same here (although I was 16 when taught because my birthday is in June, essentially bucking the trend of younger kids doing worse :D), IIRC I was with AQA for A-Level
• Nov 13th 2011, 01:47 PM
Quacky