Question

The functions f(theta)and g(theta) are sine functions where f(0) =g(0) the amplitude of f(thetha) is twice the amplitude of g(thetha) the period of f(thetha) is one half the period of g(thetha) if g(thetha) has a period of 2pi and f(pi/4)=4 write the function rule for g(thetha) explain your reasoning

Answer 1

Please someone help me

Answer 2

I've very rusty at this stuff
but i'll have a look at some notes to jog my memory

Answer 3

Okay thank you so much! @welshfella

Answer 4

here s rational - he will probably be able to help

Answer 5

okay, @rational do you have any clue? just even a guess would be fine. I just have no clue what to do with this

Answer 6

Since \(f(0)=g(0)=0\), we may "assume" that the phase shift is \(0\).
Sin we're given that the period of \(g(\theta)\) is \(2\pi\), let \(g(\theta) = A\sin(\theta).\)

Then \(f(\theta) = 2A\sin(2\theta )\) because this function has twice the magnitude and half the period of \(g(t)\) .

Answer 7

Using the given value \(f\left(\frac{\pi}{4}\right)=4\), we have
\[4=2A\sin(2*\frac{\pi}{4})\\~\\4=2A\\~\\2=A\]

Answer 8

So \(g(\theta)= 2\sin(\theta)\) is a function that satisfies the given conditions

Answer 9

Okay so how do I put this in order so I can calculate it?

Answer 10

calculate what

Answer 11

sorry that was dumb, I just have literally no clue about this problem.

Answer 12

Thank you though. do you think you could help me with one last one? this one is multiple choice. @rational

Answer 13

did u get this problem

Answer 14

the present problem
i spent so much time preparing the solution hoping it helps u

Answer 15

No not at all to be honest. I am not the best in math and this problem is just above my knowledge

Answer 16

I know I am really sorry, give me a minute I will try to figure it out.

Answer 17

@rational I just don't get what the problem is asking me for..

Answer 18

the problem is asking you to find \(g(\theta)\)

Answer 19

Okay hang on a minute

Answer 20

I just don't get it.. I am so sorry for wasting your time. I really really appriciate your effort in trying to help me @rational

Answer 21

thats okay maybe lets move on

Answer 22

So g(θ)=2sin(θ) is a function that satisfies the given conditions so this is the answer right? I just want to put something down. @rational and if you have time and the will power to work through my thick skull can you help me with one multiple choice?

Answer 23

this is a descriptive question so put everything
http://gyazo.com/15c145c9df959a23b1369628581fc453

Answer 24

Okay thank you so much. You are the best @rational

Answer 25

np