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scoundrel [369]
3 years ago
15

Need help with homework will give crown

Mathematics
1 answer:
prohojiy [21]3 years ago
6 0
For the first one it’s D.3
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Anuta_ua [19.1K]

Answer:

  A = √29

Step-by-step explanation:

The short of it is that ...

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_____

<u>Amplitude</u>

If you expand the second form using the sum-of-angles formula, you get ...

  Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Comparing this to the first form, you find ...

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  c₁ = 5 = Asin(φ)

The Pythagorean identity can be invoked to simplify the sum of squares:

  (Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²

In terms of c₁ and c₂, this is ...

  (c₁)² +(c₂)² = A²

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_____

<u>Phase Shift</u>

We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...

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  φ = arctan(5/2) ≈ 1.19029 radians

___

* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.

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3 years ago
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