The function f(theta) and g (theta) are sine functions where f(0)=g(0)=0.

Question

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

Answer 1

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 ,

f(Ø) = 10.4525 sin(Ø/2) and g(Ø) = 5.226sinØ

check:
http://www.wolframalpha.com/input/?i=y+%3D+10.4525+sin(x%2F2)+,+y+%3D+5.226sinx+for+x+%3D+0+to+15