Question

Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y = 1?

f(x) = cos(x − pi over 3) + 2

f(x) = 2 cos(x − pi over 3) + 1

f(x) = −2 cos 6x + 1

f(x) = −cos 6x + 2

Answer 1

If you require an amplitude of 2, then you'd have to eliminate the first and fourth possible answer.

Note that the period of the general sine function y = a*sin (bx + c) is \[\frac{ 2\pi }{ b }\] Perhaps this alone will be enough to help you choose the correct one of the two remaining answer choices.

"A midline at y = 1" implies that the whole cosine curve has been shifted upward by 1 unit.

Answer 2

i was leaning towards the third option...but im really not sure

Answer 3

It might help if you were to explain your own reasoning. why were you leaning towards the third option? Why would you set aside the other remaining option?

Answer 4

because there a 2 and a 3 in the question and 2x3=6 and theres a 6 in the third option...
i really dont know how to solve it :(

Answer 5

b

Answer 6

thanks, can you tell me why? @gokukamehameha

Answer 7

i did this in k12 and i remember and it was b because i picked a on my test and it was wrong it is b

Answer 8

go back to mathmale's response, and look at the equation he gave you to find the period of a sine wave

Answer 9

the problem is i dont understand anything. the only thing i know is tht cos=adj/hyp
the rest is just over my head

Answer 10

i think i'll go with b.
but thanks to everyone for all your help :)

Answer 11

np

Answer 12

What was the correct answer?

Answer 13

I think it is B as well because of the structure of a typical sin functin....but this is cosine...so...

Answer 14

I know this is extremely old, but for any future users who need help, this could help you out: https://mathway.com/examples/Trigonometry/Graphing-Trigonometric-Functions/Amplitude-Period-and-Phase-Shift?id=342