Question

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

Answer 1

From doing some current calculations. I came to the conclusion of C. Not sure if it is right or if there are anymore answers

Answer 2

\(\large\color{black}{ \displaystyle {\rm Cos}^2 (2x) - \frac{1}{4} = 0 }\)

\(\large\color{black}{ \displaystyle {\rm Cos}^2 (2x)= \frac{1}{4} }\)

\(\large\color{black}{ \displaystyle \left(~~ {\rm Cos} (2x)~\right)^2= \left(\frac{1}{2}\right)^2 }\)

Answer 3

hope that helps...

Answer 4

(take the square root of both sides, and don't forget the \(\pm\) )

Answer 5

Ok! I will try to solve from there and I'll tell you what I get

Answer 6

sure:)

Answer 7

(oh, there is only 1 incorrect option)

Answer 8

So \[\cos(2x) = \pm \frac{ 1 }{ 2 }\] 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?

Answer 9

So there are 3 correct answers?

Answer 10

yes

Answer 11

30 degrees is one of them (as you said)

Answer 12

Ok! Now I do not know where to do from here

Answer 13

We already have \[\frac{ \pi }{ 6}\] as one answer

Answer 14

you 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.

Answer 15

yes π/6 is correct

Answer 16

I don't think I plugged the numbers in properly, but I got 12pi/6 and 5pi/6?

Answer 17

12π/6 is not right

Answer 18

5π/6 is right

Answer 19

Ok! So how would I plug them in? I know I did it wrong haha

Answer 20

(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)

Answer 21

you would just plug the answer choices instead of x, into that equation
cos²(2x)-1/4=0

Answer 22

Oh and what gets you = 0 right?

Answer 23

\[2 \cos ^22x=\frac{ 1 }{ 2 }\]
\[1+\cos 4x=\frac{ 1 }{ 2 }\]
\[\cos 4x=\frac{ 1 }{ 2 }-1=-\frac{ 1 }{ 2 }=-\cos \frac{ \pi }{ 3 }=\cos \left(2n \pi+ \pi \pm \frac{ \pi }{ 3 } \right)\]
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,....

Answer 24

cos(4x) :) I haven't thought of that one....

Answer 25

So the answers would be \[\frac{ 5\pi }{ 6}, \frac{ 11\pi }{ 3 }, and \frac{ \pi }{ 6 }?\]

Answer 26

yes.
use ~ for space

Answer 27

yw

Answer 28

Thank you for your time and the tips :)