Question

how do you find both solutions of cos(x)=1/3

Answer 1

Here's a handy little table from a page on my website:
http://www.1728.org/trigtutr.htm

Answer 2

Wow this question is still open?
Okay, basically you are being asked to find the arc cosine of 1/3.
(In other words you must find an angle whose cosine = .333333)
You could use a log table but you might have a calculator with trig functions.
See if one of the keys says arc cos or something like that.
Anyway, the arc cosine of 1/3 is 70.529 degrees.

Now to get that second value, we look at the attachment I posted.
It says to call the first angle we calculated angle y which equals 70.529°
To find the second angle, it says to subtract angle y from 360°
360° - 70.529° = 289.472°
Now you have both angles.