vera_ewing
  • vera_ewing
What cosine function represents an amplitude of 3, a period of π, no horizontal shift, and a vertical shift of 2?
Mathematics
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vera_ewing
  • vera_ewing
What cosine function represents an amplitude of 3, a period of π, no horizontal shift, and a vertical shift of 2?
Mathematics
chestercat
  • chestercat
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Michele_Laino
  • Michele_Laino
hint: the amplitude of your function is 2, since we have: \[ - 2 \leqslant 2\cos \left( {\pi x} \right) \leqslant 2\]
Michele_Laino
  • Michele_Laino
the requested function is like below: \[y = A\cos \left( {\frac{\pi }{k}} \right) + h\] where A is the amplitude, h is the vertical shift, and k is such taht the period of that function is: \[T = \frac{{2\pi }}{k}\]
Michele_Laino
  • Michele_Laino
that is the general formula, for your exercise

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vera_ewing
  • vera_ewing
So it's going to have to start out as f(x)= 3cos right?
Michele_Laino
  • Michele_Laino
yes!
vera_ewing
  • vera_ewing
And the last part of the equation will be +2?
Michele_Laino
  • Michele_Laino
yes!
Michele_Laino
  • Michele_Laino
oops.. I have made a typo, here is the right formula: \[y = A\cos \left( {\frac{x}{k}} \right) + h\]
vera_ewing
  • vera_ewing
f(x) = 3 cos 2x + 2 ?
Michele_Laino
  • Michele_Laino
yes! that's right!
vera_ewing
  • vera_ewing
Thank you, Michele! :)
Michele_Laino
  • Michele_Laino
thanks! :)

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