Question

Find the value of a so that the period(T) of the function y=cos^2[(a^2+2a-28)*x)] would be T=PI/20

Answer 1

which is the variable x or a??

Answer 2

I'm not actually sure, but I think it might be x.

Answer 3

a is supposed to be a parameter.

Answer 4

i don't think you will get time period so easily ... if there is a general term a if x is a variable.

Answer 5

In which case the problem would make sense the most?

Answer 6

sorry, i didn't read the question properly

Answer 7

Oh, alright.

Answer 8

(a^2+2a-28) = pi/20
or, (a+1)^2 = pi/20 + 29
now solve for a

Answer 9

And that's it?

Answer 10

yes,
http://www.wolframalpha.com/input/?i=y%3Dcos%5E2%5B10*x%29%5D+

Answer 11

Alright, thanks!

Answer 12

I /think/ is you have a trig function of the form y = cos(Ax), then it's period is given by \(\frac{2\pi}{A}\).
so first you need to convert the \(\cos^2\) function into one which does not involve powers. I believe you can use this formulae:\[\cos^2(x)=\frac{\cos(2x)+1}{2}\]

Answer 13

replace "is" with "if" after "/think/" above

Answer 14

so you would end up with:\[\cos^2((a^2+2a-28)x)=\frac{\cos(2(a^2+2a-28)x)+1}{2}\]

Answer 15

and to get a period of \(\frac{\pi}{20}\) you need to solve:\[\frac{2\pi}{2(a^2+2a-28)}=\frac{2\pi}{20}\]

Answer 16

And the a value I get is the answer?

Answer 17

yes - you should get two values since this is a quadratic equation

Answer 18

sorry - I made a mistake up there, the right-hand-side should be \(\frac{\pi}{20}\)

Answer 19

not \(\frac{2\pi}{20}\)

Answer 20

Oh, alright. Thanks!

Answer 21

yw

Answer 22

period was already changed by half when you made it 2x

Answer 23

no - I just rewrote cos^2(x) in terms of cos(2x)

Answer 24

the resulting equation is still the same equation, so we still need it to have the same period

Answer 25

quite not ... the period of [cos(x)]^2 will be 2pi while period of cos(2x) will be pi
it seems that way.
http://www.wolframalpha.com/input/?i=y%3Dcos%5E2%5B10*x%29%5D+
the time period of this expression still seem to be 2pi/x
http://www.wolframalpha.com/input/?i=y%3D+%28cos%5B20*x%29%5D+%2B1%29%2F2++
while isolating this expression will change the time period by pi/x
http://www.wolframalpha.com/input/?i=y%3Dcos+%5B20*x%29%5D+

Answer 26

experimentX: do you agree that:\[cos^2(x)=\frac{cos(2x)+1}{2}\]

Answer 27

yeah i agree, the both expression on the right hand side and left hand side will have the same time period,

Answer 28

so what are you trying to say then? I don't understand?