for part (a) use the identity
and then you'll have it in terms of sin
Hello,
Here is a pre calculus problem I am having trouble with. The problem is from a review sheet for pre calculus, but I do not recall doing anything like this in my pre calculus class.
(a) Express the function in terms of sine only.
(b) Find the amplitude A, period P, and phase shift B of the function, and graph one complete period.
Any help is greatly appreciated.
Thanks
What razorfever said for part (a) is fine, and you will get an answer in terms of sine that is correct, however, the form that you will get likely will not be one that helps you in part (b) a lot.
alternatively, note that there is a formula that goes like this (i do not know what it's called, or if it even has a name), but it is based on the addition formula for sine.
here, are constants.
basically, here (if we write 2 instead of x), and we want to find and to have a nice form in sine that we can graph easily and find all the things we are required to find. first, we will modify the formula, to write 2x instead of just x.
so here goes:
.............by the addition formula for sine
note that here we have
...........(1)
.........(2)
thus we have two simultaneous equations, with two unknowns, we can solve for our unknowns. (try doing that yourself, it can come in handy to recall )
anyway, there are infinitely many solutions here, any one will suffice. the nicest one i think is: ,
thus, we have:
or in other words,
can you take it from here?
EDIT: in retrospect, it would perhaps have been easier to note the following: