Question

f(x)=2cos(x)in the interval 0 is less than or equal to x less than or equal to 2 pi. if g(x) is a shift of f(x) a distance of pi over 2 to the right, write an equation for g(x). anyone know????

Answer 1

All you would want to do is shift the x on the inside. So g(x)=2cos(x-2). So this takes whatever x value you have, removes two from it, and moves it two over from where it would normally be (f(x)).

Answer 2

2cos(x-pi/2)

Answer 3

yes, it will be
\[f(x)=2\cos(x-\frac{\pi}{2})\]better known as \[sin(x)\]

Answer 4

Sorry, I didn't see the pi/2 D: But yes, g(x)=2cos(x-(pi/2))

Answer 5

i should say better known as \[2\sin(x)\]

Answer 6

both maleviolence and sleek-feathered one (?!) are right, but you should convince yourself that
\[\cos(x-\frac{\pi}{2})=\sin(x)\]

Answer 7

thank you everyone! and then the next one is to write an equation involving no shift. would that be 2sin(x)?

Answer 8

confused. if it is no shift then wouldn't it be the original function?

Answer 9

yeah im confused to. idk i think it would be a 2sin(x) but im not sure

Answer 10

what does the question say exactly?

Answer 11

sin(x) and cos(x) are complimentary functions which means if you subtract 90 degrees (the compliment) you get the other function. so cos(x-(pi/2))=sin(x)

Answer 12

To see this, graph sin(x) and cos(x) and notice that one is shifted pi/2 from the other.

Answer 13

ohh ok gotcha, thank you

Answer 14

No problem :P

Answer 15

you can also show this using the "addition angle" formula if you got there yet