Question

A person who was listening to a siren reported that the frequency of
the sound fluctuated with time, measured in seconds. The minimum
frequency that the person heard was 500 Hz, and the maximum
frequency was 1000 Hz. The maximum frequency occurred at t=0
and t=15 . The person also reported that, in 15, she heard
the maximum frequency 6 times (including the times at t=0 and
t=15). What is the equation of the cosine function that describes
the frequency of this siren?

Answer 1

y= a cos K(x-d)+c
a=250
period= 15s?

Answer 2

the equation is

y = A cos [2pi/period( x - p.s.) ] + v.s.

A =( max - min )/ 2
v.s. = ( max + min) / 2

period here is 15 / 5 seconds, since she heard the maximum 6 times (and that is 5 complete cycles)
there is no phase shift or horizontal translation since she starts at the maximum , and cosine starts at a maximum.

y = 250 cos ( 2pi/3 ( x - 0) ) + 750
y = 250 cos ( 2pi / 3 *x ) + 750