y=1747.29+1636.95sin(0.52x-1.71).  What is the period for this function? and if you know the y value how do you figure out the x value?

For the first question I know that to get the period you do 2pi/k but that does not give me a whole number such as 10 or 5, instead i get a number multiplied by pi which is not what i want.  For the second question I figured out that at x=3.6 y=2011.32 and now I am asked to figure out more x values with the y value equal to 2011.32 using this equation, so i plugged in 2011.32 in for y and now i don't know what to do.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We are given `y=1747.29+1636.95sin(.52x-1.71)`

(1) You are correct about the period. The period will be `p=(2pi)/.52=(50pi)/13~~12.083` This is what it is -- we might like to have "nice" answers but that rarely happens in the real world. The problem is what value to approximate to.

(2) If y=2011.32:




(a) `"Sin"^(-1)(sin(.52x-1.71))="Sin"^(-1)(.1612938697)`



`x=3.600002978` thus your answer of x=3.6

(b) When using the arcsin (inverse sin) there is the possibility that the angle is in another quadrant, so you also have:





Thus to a good approximation we have two points where the y value is 2011.32: x=3.6 and x=9.02.

To find more, we add the period to the two possible answers:

`y=2011.32==>x~~3.6+-12.083`  or `x~~9.018+-12.083`

The graph:

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial