values of x

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• May 30th 2005, 06:13 AM
slurch901
values of x
hey all,

if -pie < x < pie, find all values of x if cos 2x = 0.5

anyone know this one???
• May 30th 2005, 09:34 AM
Math Help
should be $\pm\frac{pi}{6}$and $\pm\frac{5pi}{6}$
• May 30th 2005, 12:35 PM
slurch901
that sounds about right, lol but how do you get it? I sort of need a step by step or it will annoy me for ages :S
• May 30th 2005, 06:11 PM
Math Help
Unit circle
I would think about the unit circle. And how cos is the x values. Then try and find the two angles that will get you a value of .5 and divide them by two since we are talking about cos(2x).

Also you have to think about negative values by going clock wise instead of counter clock wise.
• Jun 18th 2005, 08:14 AM
slurch901
i have got you so far...., the to angles are 30, and -30 after dividing 60 by 2, buy, the angles are supposed to be between -pi and pi :S.... is there a next step or something :)
• Jun 18th 2005, 10:06 AM
Math Help
Yes
cos of 300 degrees and 300 degrees will also give you 0.5.
Since it is cos(2x) your last two answers are 150 and -150 and those fall between -pi and pi.
• Jun 19th 2005, 08:29 AM
slurch901
soz for being a pain lol, but since when is -150 and 150 between -3.14 and 3.14????
• Jun 19th 2005, 10:03 AM
MathGuru
Radians and Degrees
The problem here is that we have confused the units of angle.

3.14 or pi is referring to radians
180 degrees is in degrees

3.14 radians = 180 degrees

so 150 is inbetween -180 and 180.

The unit circle in the above post is with degrees units when your question was stated with radians in mind. If you look back to the initial posts those answers are still correct:)
• Jun 19th 2005, 01:59 PM
slurch901
thx for that :). The guide that ui using is absolutly useless, so onc e again thx for clearing that up :)