A cosine function has a period of (6π)/5, an amplitude of 5, and a vertical translation 6 units down. The function is not reflected over the x-axis. What is the equation for this cosine function?
f(x)= [ ] cos( [ ] x) [ ]
Select and put answers into the appropriate spot of the equation. There should be 3 answers.
[ 3π / 5 ] [ 6/5 ] [ 5 ] [ 5/3 ] [ -6 ] [ 6π / 5 ] [ -5 ] [ -6 ] [ 3/5 ] [ 5π / 3 ]
I got f(x)= [ 5 ] cos( [ 6π / 5 ] x) [ -6 ]. The only thing that's really having me second guess myself is the period. When I graph the equation, I get 5/3 as the period. If someone could help me understand why or correct me, I'd appreciate that a lot.
We have this form :
y = A cos (Bx) + C
A = the amplitude = 5
B = 2pi / period = 2pi [ (6/5) pi ] = 2 / (6/5) = 2 (5/6) = 10/6 = 5/3
C = the vertical shift = -6