Hi
The maximum possible value for a cosines is 1 and the minimum is -1
Therefore
a + d = 29
-a + d = 15
which leads to a = 7 and d = 22
Hi,
I have a maths exam tomorrow, so I would be grateful for any help!
So here it is:
Let f(t) = a cos b(t-c) + d (I understand that this refers to the transformation)
when t = 3, there is a maximum value of 29,
when t = 9, there is a minimum value of 15.
Find the value of a.
I got as far as:
29 = a cos 3t
15 = a cos 9t
Is that right? And how should I find a?
Thanks!
No, I don't think that's right. Remember that assumes values in the range . If you assume that , you get that the largest value of is going to be and the smallest value is going to be . Hence a and d have to satisfy two equations: and , from which you get the correct values for a and d.
Next you must understand that this problem has infinitely many solutions. This is because, the distance between the t coordinates of a minimum and a maximum must be half the period (plus, optionally, an integral multiple of the period) of . This allows you to determine the (infinitely many possible) value(s) of , because the period of satisfies the relation .
Given the right value for you can now choose the correct value for by noting that you just have to shift the the graph by 3 units to the right in the x-direction.