# Radians and surds

Printable View

• Aug 8th 2006, 08:58 AM
kendon
Radians and surds
Having problems with working out surds from radians. Does anyone now the whereabouts on the net where there is an extensive chart? At the moment i am struggling with cos(5*pi/6).
Cheers in advance
• Aug 8th 2006, 09:04 AM
ThePerfectHacker
Quote:

Originally Posted by kendon
Having problems with working out surds from radians. Does anyone now the whereabouts on the net where there is an extensive chart? At the moment i am struggling with cos(5*pi/6).
Cheers in advance

You got a calculator? Good.

Your problem is this, you need a way to express trigonometric functions of certain angles in radical form. I remember when I was in 11th grade my cl*** was going insane with this so I have a trick which you can do.
For example,
$\cos \frac{5\pi}{6}=-0.86602541$
Now, if you end up with a long decimal square,
$(-0.86602541)^2=.75$
But,
$.75=\frac{3}{4}$
Now, that the square root back.
$\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$
Important. When you square the sign always goes away. Therefore, if you had a sign in the beginning (and you did) when you need to attach a sign here.
• Aug 8th 2006, 09:16 AM
CaptainBlack
Quote:

Originally Posted by kendon
Having problems with working out surds from radians. Does anyone now the whereabouts on the net where there is an extensive chart? At the moment i am struggling with cos(5*pi/6).
Cheers in advance

An angle of $5 \pi/6=-\pi/6$, now $\pi/6$ is 30 degrees, and so its cosine is $\sqrt{3}/2$ (consider the sides
of half of an equilateral triangle), and the cosine function is even so

$\cos(5 \pi/6)=\cos(-\pi/6)=\cos(\pi/6)=\sqrt{3}/2$

RonL