Question

Find the amplitude, frequency, and distance when t=3

a. y=-15cos((pi*t)/3)+5

b. y=120sin100pi*t

I think the amp for a. is 15, the freq is 3/2 cycles per unit of time, and the distance is 20, but I'm not totally sure if I'm approaching this problem correctly.

Answer 1

(a)
The period is (2pi) / (pi/3) = 6
so, the frequency is 1/6

your amplitude and distance are correct.

Remember, the period for cos(kt) is 2pi/k

So, (b) should be no trouble now.

Answer 2

Why isn't it (2pi) / (3pi) or (2pi) / (3), since the problem asks when t=3?

Answer 3

the period and amplitude do not change, whatever the value of t. The question asks for three things:

amplitude
frequency
distance when t=3

The distance when t=3 is

y(3) = -15cos((pi*3)/3)+5
= -15cos(pi)+5
= 15+5
= 20