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anonymous
 one year ago
Which of the following are solutions to the equation
cos^2 (2x)  1/4 = 0?
Check ALL that apply.
A. 5 pi/ 6
B. 11pi / 3
C. pi / 6
D. 12pi / 6
anonymous
 one year ago
Which of the following are solutions to the equation cos^2 (2x)  1/4 = 0? Check ALL that apply. A. 5 pi/ 6 B. 11pi / 3 C. pi / 6 D. 12pi / 6

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0From doing some current calculations. I came to the conclusion of C. Not sure if it is right or if there are anymore answers

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle {\rm Cos}^2 (2x)  \frac{1}{4} = 0 }\) \(\large\color{black}{ \displaystyle {\rm Cos}^2 (2x)= \frac{1}{4} }\) \(\large\color{black}{ \displaystyle \left(~~ {\rm Cos} (2x)~\right)^2= \left(\frac{1}{2}\right)^2 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1hope that helps...

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(take the square root of both sides, and don't forget the \(\pm\) )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok! I will try to solve from there and I'll tell you what I get

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(oh, there is only 1 incorrect option)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So \[\cos(2x) = \pm \frac{ 1 }{ 2 }\] If I remember how to do this properly, I think I find what 1/2 is on the unit circle, which would be 60? Then divide 60 by 2 and get 30 degrees?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So there are 3 correct answers?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.130 degrees is one of them (as you said)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok! Now I do not know where to do from here

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We already have \[\frac{ \pi }{ 6}\] as one answer

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you can plug the rest of the options, if you don't want to go ahead and generate the solution sets for 1/2 and +1/2.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes π/6 is correct

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think I plugged the numbers in properly, but I got 12pi/6 and 5pi/6?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.112π/6 is not right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok! So how would I plug them in? I know I did it wrong haha

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(click alt, and hold it click 2 2 7 respectively on your number pad on the left if you have one release alt: you get π)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you would just plug the answer choices instead of x, into that equation cos²(2x)1/4=0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh and what gets you = 0 right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[2 \cos ^22x=\frac{ 1 }{ 2 }\] \[1+\cos 4x=\frac{ 1 }{ 2 }\] \[\cos 4x=\frac{ 1 }{ 2 }1=\frac{ 1 }{ 2 }=\cos \frac{ \pi }{ 3 }=\cos \left(2n \pi+ \pi \pm \frac{ \pi }{ 3 } \right)\] where n is an integer. \[4x=\left( 2n+1 \right)\pi \pm \frac{ \pi }{ 3 }\] \[x=\frac{ 1 }{ 4 }\left\{ \left( 2n+1 \right)\pi \pm \frac{ \pi }{ 3 } \right\}\] now you can check by plugging n=0,1,2,....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1cos(4x) :) I haven't thought of that one....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the answers would be \[\frac{ 5\pi }{ 6}, \frac{ 11\pi }{ 3 }, and \frac{ \pi }{ 6 }?\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes. use ~ for space

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for your time and the tips :)
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