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vera_ewing

  • one year ago

What cosine function represents an amplitude of 3, a period of π, no horizontal shift, and a vertical shift of 2?

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  1. Michele_Laino
    • one year ago
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    hint: the amplitude of your function is 2, since we have: \[ - 2 \leqslant 2\cos \left( {\pi x} \right) \leqslant 2\]

  2. Michele_Laino
    • one year ago
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    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: \[T = \frac{{2\pi }}{k}\]

  3. Michele_Laino
    • one year ago
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    that is the general formula, for your exercise

  4. vera_ewing
    • one year ago
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    So it's going to have to start out as f(x)= 3cos right?

  5. Michele_Laino
    • one year ago
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    yes!

  6. vera_ewing
    • one year ago
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    And the last part of the equation will be +2?

  7. Michele_Laino
    • one year ago
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    yes!

  8. Michele_Laino
    • one year ago
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    oops.. I have made a typo, here is the right formula: \[y = A\cos \left( {\frac{x}{k}} \right) + h\]

  9. vera_ewing
    • one year ago
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    f(x) = 3 cos 2x + 2 ?

  10. Michele_Laino
    • one year ago
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    yes! that's right!

  11. vera_ewing
    • one year ago
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    Thank you, Michele! :)

  12. Michele_Laino
    • one year ago
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    thanks! :)

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