Answer:
C
Step-by-step explanation:
Hello!
In the equation y=a cos bx, we can learn alot about the cosine graph.
a is the amplitude, or how 'long' the cosine graph is.
b is the period, which is how 'wide' one cycle of a cosine period can be. The higher the period, the wider the cycle is.
In this equation, we are focused on finding the period; so any choices that contain amplitude is not a correct answer choice for this problem, which leaves out B and C.
To find the period, we can plug b into [tex]\frac{2\pi }{b}[/tex] , which in a way converts the b value to a period.
For B) y= cos3x
[tex]\frac{2\pi }{3}[/tex]= it does not equal 3 [tex]\pi[/tex]
For C) y=cos [tex]\frac{2}{3}[/tex]x
[tex]\frac{2\pi }{\frac{2}{3}}[/tex]= equals 3 [tex]\pi[/tex] when simplified
Since C equals 3 [tex]\pi[/tex] as a period, C is the only logical answer.
