Thread: 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

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,
$\displaystyle \cos \frac{5\pi}{6}=-0.86602541$
Now, if you end up with a long decimal square,
$\displaystyle (-0.86602541)^2=.75$
But,
$\displaystyle .75=\frac{3}{4}$
Now, that the square root back.
$\displaystyle \sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$
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.

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

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

RonL