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`a \sin(wt + phi ) = c2 \sin(wt)+ c1 \cos(wt)`use the information above and the trigonometric identities to prove that Asin(wt+phi)=c2sin(wt)+c1cos(wt)​

Answer 1

Explanation:

In order to prove that Asin(ω⁢t+ϕ) equals c2sin ω⁢t+ c1cos ω⁢t we need use the sin (A+B) sum identity.

The sin sum identity is sin(A+B)= sinA × cosB + cosB × sinA

Now lets plug in our info.

Asin(ω⁢t+ϕ)= (sin wt × cosϕ) + (cos wt × sinϕ)

We know that Asin= c1 and Acos= c2.

Once we input c1 and c2 and solve, our end result becomes c2sin(wt)+c1cos(wt)​

Answer 2

Answer and Step-by-step explanation:

Given Asin(wt + phi), we know that sin (A + B) = sinAcosB + sinBcosA. This means:

Asin(wt + phi) = Asin(wt)cos(phi) + Asin(phi)cos(wt).

Let Acos(phi) = c2 and Asin(phi) = c1 we have:

Asin(wt + phi) = c2sin(wt) + c1cos(wt)