Write y(t)=2sin4πt+5cos4πt in the form y(t)=asin(wt+φ) and identify the amplitude, angular frequency, and the phase shift of the spring motion. record your answers in the response box.

Angular frequency:

Phase shift:

Amplitude:

Step-by-step explanation:

Trigonometric Transformations

There's a number of trigonometric identities that can help us to transform expressions into others more useful or convenient. One well-known relation is the sine of the sum of angles:

We also know

We are given the expression

and are required to transform to the form

Where A,w and must be determined. We apply the formula for the sine of the sum of angles

This must be equal to the given expression

Being the phase shift and therefore independent of time, we can safely equate term to term

The time-dependant parts are equal, so

a)

Both relations give us the angular frequency w

Now the rest of the equations allow us to find \phi and A

Taking squares of both and adding them

Given that

We have

Dividing [2] by [1]

Or

Summarizing

Angular frequency:

Phase shift:

Amplitude:

answer:

step-by-step explanation:

here, the total dishes = 10

dishes having meat = 3 ( chicken, meatloaf and hamburger )

thus, the probability of having meat on the chosen dishes = number of dishes having meat / total dishes

=

therefore, the probability of not having meat = 1- the probability of having meat on the chosen dishes

=

=

=

⇒ option b is correct.