Hey need some help with a question:
If cosx=−cos(π6) and π2 < x < π find the value of x.
Please explain, don't really get it. Thanks in advance
Hey there Oynx!
Did you mean
or
I'm guessing the second one, for one thing, cos(u) = cos(-u); for another thing, cos(u) = -cos(u + pi)
So
Assuming I didn't make any silly mistakes.
(and then it's pretty obvious x is 5pi/6) both properties used there should be fairly obvious from just, like, looking at the unit circle.
Hope this makes sense, if it doesn't don't hesitate to ask!
EDIT: Just in case if anybody is confused.
The reason behind it is because of the different quadrants, because if you did 180 - 60 = x for the second question you would get 120, which doesn't satisfy 180 < x < 270.
Start by thinking about what -cos(60) is on the unit circle; cos(60) is the horizontal distance at 60 degrees, so "negative" of that is reflecting 60 degrees across the middle which gives you cos(180 - 60) = cos(120), which is the first one but cos is horizontal distance, and there are two points on the other side of the unit circle with that. Because if you change the vertical distance only, the horizontal distance is the same and the point with the same horizontal distance but different vertical distance you can get by reflecting it over the other axis, the x axis. Reflecting over the x axis you can think of as negating the thing on the inside, so cos(-120), and then add 360 because negative numbers are inconvenient and you get 240.