I am having trouble with the following trigonometry problem:
cos2x= -1/2
I tried to turn cos2x into 2cos^2x-1 according to the double angle identity, but then I was unable to factor the problem. Where have I gone wrong, or where do I go from here?
![]() |
I am having trouble with the following trigonometry problem:
cos2x= -1/2
I tried to turn cos2x into 2cos^2x-1 according to the double angle identity, but then I was unable to factor the problem. Where have I gone wrong, or where do I go from here?
I'm not sure why you need the identity. Can't you solve it like this or isn't it allowed?
![]()
![]()
I guess you could do it this way:
And now you have two roots and you still have to take the ArcCos, so you haven't gained much.
My math tell me that
x= 60 and 120 degrees... for 0 < x < 360
BUT if you do through identity, x = 30, 60, 120 and 150 for 0 < x < 360
I'm confused. Cos(60) = 0.5, not -0.5. You need to be in the 2nd or 3rd quadrant for it to be -0.5. So 2x = ±120 (or 240), x=±60 on 0 < x < 360. Oh. I guess that does give x=120 also. My bad. 30 degrees and 150 degrees certainly don't fit the original problem, however.
Perito, when I turned in my homework, I found cos x= 1/2 without the identity as you worked it and then I found my solution set, but I got it wrong.
Hmmm. :mad: What answer was said to be the correct one?
Yeah, I know that those do not fit in the original question... :o was just posting just in case there was a need for passing through trig identity.
Ok, edited my first post in the thread...
Or was it in rads? Then the answers would beQuote:
Perito agrees: Good. I wonder why they marked her wrong.
or
1.05 , 2.09
All times are GMT -7. The time now is 12:11 AM. |