How do I calculate the instantaneous voltage?

Question

A sine wave voltage has a maximum value of 12 V and a frequency of 80 Hz. Calculate the instantaneous voltage at 10 ms.

It's a multiple choice question and the following choices are:

A. -11.4 V

B. 0 V

C. 1.05 V

D. -3.84 V

E. 0.09 V

I wasn't sure how to go about this question so I picked C but it was wrong.

Answer 1

My choice is A for the following reason.

The voltage will have a general form of Asin(kt + p).

1) The amplitude, A, is the maximum voltage, which is given as 12 V.

2) The constant k is computed from the given frequency of 80Hz.

That implies period of 1000/80 = 12.5 ms.

That means that when t = 12.5, kt = 2π(which is the period of sin).

From that

k = 2π/12.5

3) The phase p is not mentioned in the problem, so

the most reasonable choice is p = 0.

Thus we need to evaluate the resulting function at t = 10ms:

12sin(2π10/12.5) = -11.4