The function f(theta) and g (theta) are sine functions where f(0)=g(0)=0.
The amplitude of f (theta) is twice the amplitude of g(theta).
The period of f(theta) is one-half the period of g(theta).
If g (theta) has a period of 2pi and fpi/4=4. Write the function rule for g(theta)
Explain your reasoning.
I'm 70 years old and lost here. Any help would be appreciated
let g(Ø) = asin kØ
so the amplitude is a and p= 2?/k
then f(Ø) = 2a sin (kØ/2)
check: period of of g(Ø) = 2?/k
period of f(Ø = 2?/(k/2) = 4?/k , which is twice that of g(Ø)
but we are told that 2?/k=2?
so k = 1
so far we know:
g(Ø) = a sin Ø and f(Ø) = 2a sin (Ø/2)
we still need "a"
given f(?/4) = 4
2a sin ?/8 = 4
2a (.38268) = 4
2a = 10.4525
a = 5.226 ,