00:01
If you're asking for a 2 sine squared of 3x minus 1 is equal to 0, the first thing that you would want to do is get sign by itself.
00:14
And hopefully it makes sense that if this is a quantity that you understand that you add 1 to 0 and then divide by 2 because it's a multiplication problem.
00:24
So then your next step would be to square root both sides.
00:27
Now make sure that when you square root that you get a positive.
00:31
And a negative answer, square root of each of those pieces.
00:35
And the square root will cancel out the square.
00:37
And what you'll probably want to do is rationalize this denominator by multiplying top and bottom by root 2.
00:44
1 times root 2 is root 2 and root 2 times root 2 is root 4, which reduces to 2.
00:50
So then on the unit circle, what you're asking yourself is where to sign equal root 2 over 2.
00:58
And sign is positive in the first and second quadrant at pi over four and three pi over four but then sign is also negative root 2 over 2 in the third and fourth quadrant at 5 pi over 4 and 7 5 pi over 4 and you might need to look at a unit circle for that so we have 3x is equal to those values but here's the thing is if you have a 3 right here you actually have to do three revolutions.
01:45
And the reason why you have to do three revolutions is we're about to divide everything by three.
01:50
And by doing a full revolution, how about this? if i do two revolutions and i divide it by three, we're going to take one third of that away.
01:59
And we'll get back into the interval that they asked you for from zero to two pi...