f(x) is a sinusoidal function with domain (-∞,∞) , with a period of 120, an amplitude of 1 and a midline of y = -1 . Assume that f(x) attains its minimum value at x=3 .

Question

f(x) is a sinusoidal function with domain (-∞,∞), with a period of 120, an amplitude of 1 and a midline of y = -. Assume that f(x) attains its minimum value at x=3

.  

f(3)=?

f(63)=?

 

f(423) =?

Answer 1

amplitude of 1 means y varies from 3 to 5 with midlne y=4

f(x) =A(Bsinx + C) + D where A=amplitude D = midline, C = phase shift, B involves the period or frequency

f(x) =sinBx +C + 4

the period = 120 then 360/B = the period. 360/B = 120, B = 3, frequency is 3 times the frequency of sinx. The graph of sinx is compressed like a spring

f(x) = sin(3x+C) + 4

f(3) = 3

f(3) = sin(9+C) + 4 = 3

sin(9+C) =-1

9+C = 270

C = 270-9 = 261

f(63) = sin(189+261) + 4

= sin450 +4

=sin(450-360) + 4

= sin90 +4

= 1 +4

=5

f(423) = f(423-360) = f(63) = 5

assuming x is measured in degrees. Since the arithmetic calculations came out to simple integer solutions suggests degrees were intended