+0

Help would be greatly appreciated! My answer is at the bottom, but I just want to be sure I'm right :)

+1
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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.

Mar 24, 2020

#1
+111330
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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

Mar 24, 2020
#2
+224
+2

Thank you so much! I appreciate the fast response!

So, correct me if I'm wrong, but 2pi / period is always used to get B in the equation?

Mar 24, 2020
#3
+111330
+1

Yep.....always true

B =  2pi  / period

CPhill  Mar 24, 2020