To rewrite y(t) = 2 * sin (4 pi t) + 5 * cos (4 pi t) in the form Asin(wt+phi), you must first find the amplitude. Use c1=Asin(phi) and c2=Acos(phi) along with the Pythagorean identity to solve for A (amplitude.) previous question: By plugging in for c1 and c2, the equation should shift to be: Asin(wt+phi)=Acos(phi)sin(wt)+Asin( phi)cos(wt) Use the identity sin(x+y)=sin(x)cos(y)+cos(x)sin(y)

The equation in standard form is .

Step-by-step explanation:

We use the following trigonometric identity:

, (Eq. 1)

If we have formula , by direct comparison with (Eq. 1):

(Eq. 2)

(Eq. 3)

Where:

- Amplitude, dimensionless.

- Phase angle, measured in radians.

By dividing (Eq. 3) by (Eq. 2), we get that:

From (Eq. 2) we find the amplitude:

Therefore, we find that equation in standard form is:

(Eq. 4)

Where is the angular frequency, measured in radians per second.

(, , )

ddd

step-by-step explanation:

p

step-by-step explanation: