Question

The functions 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 f(pi/4) = 4, write the function rule for g(theta).

Answer 1

The period of \(f(\theta)\) is one-half the period of \(g(\theta)\)
the period of \(g(\theta)=2\pi\)

Answer 2

what is the period of \(f(\theta)\) ?

Answer 3

so the period of f(theta) is pi

Answer 4

yes

Answer 5

so you know that \(f\) had period \(\pi\) and that \(f(0)=0\) which means that \(f(\pi)=0\) as well

Answer 6

there is my lousy picture of \(y=f(\theta)\)
the period is \(\pi\) and you know that \(f(\frac{\pi}{4})=4\)

Answer 7

this tells you the amplitude is also \(4\) so you should be on your way to determining the function \(f\)

Answer 8

let me know if you get stuck

Answer 9

so if the amplitude is 4, the period is pi, what does that make the function for f? y = 4 sin, then what?

Answer 10

\(y=4\sin(bx)\) you have to determine \(b\) using the fact that the period is \(\pi\)

Answer 11

2pi/pi = 2. b is 2?

Answer 12

yes

Answer 13

so y = 4 sin (2x), right?

Answer 14

yes

Answer 15

so the start of function g = y = 2 sin to start. if the period of g is 2pi, then 2pi/2pi = 1? sp y = 2 sin (1x)?

Answer 16

looking more closely at your question, i am wondering if you had a typo there

Answer 17

let me look more carefully
it seems you are being asked only for the function \(g\) not the function \(f\)

Answer 18

i retyped the question from my assignment, here's a screenshot of the question in case i typed something incorrectly: http://puu.sh/3cJDy.png

Answer 19

yes only the function of g, but to find the function of g i needed to know the function of f

Answer 20

ok good