Question

For a sine function with amplitude A=0.75 and period T=10, what is y(4)?

I'm so confused, please help!! It's for my AP Physics summer assignment, and I haven't learned this yet.

Answer 1

`y(4)=0.033`

Explanation:

.

The general form of a sine function is:

`y=asin(bx+c)`

where `a` is the amplitude, `b` is the coefficient of the angle, and `c` is the phase shift.

To find the period of the function, we have to divide the regular period of a sine function, which is `2pi`, by the coefficient of the angle.

Therefore, the period of the above general sine function would be:

`(2pi)/b`.

In this problem, the period is given as `T=10`. This means:

`(2pi)/b=10`

`2pi=10b`

`b=pi/5`

If we assume there is no phase shift. i.e. `c=0` then our sine function would be:

`y=0.75sin(pi/5x)`

`y(4)=0.75sin(pi/5(4))`

`y(4)=0.75sin((4pi)/5)=0.75(0.044)=0.033`