What are the period and phase shift in the function y=4sin(3X+Pie/4)-2?

[Ry122]

In the function
y=4sin(3X+Pie/4)-2
what determines the period and phase shift?
I know that 4=Amplitude
The answer in the back of the textbook says
Period=2pie/3
Phase Shift=-pie/12

 

[mjsd]

standard form:
$$A\sin (kx+\phi)$$
period is given by $$2\pi/k$$

 

[sutupidmath]

standard form:
$$A\sin (kx+\phi)$$
period is given by $$2\pi/k$$

Yeah but i think it is better to do it this way, because not always you can immediately determine the period of a function based on that standard form. I think it is better to first know how to come up to that standard form.

so how do we know whether a function is periodic or not?

f(x+T)=f(x), where T is the period.
so after you substitute these values you will be able to find the period of that function, which is the same as ry122 said on his op.

 

[ChaoticLlama]

dessert =/= a mathematical constant, Ry