How do you find the amplitude and period of #y =cos6x#?

1 Answer
Gió
Aug 5, 2015

I foun:
Amplitude #A=1#;
Period #pi/3#

Explanation:

Your equation is in the form #y=Acos(kx)#
Where:
#A=#amplitude; in your case #A=1#;
#k=(2pi)/(period)#; so that in your case:
#period=(2pi)/k=(2pi)/6=pi/3#.
Your #cos# function will oscillate between #+1 and -1# and complete an entire oscillation, say, between zero and #pi/3=1.05#.
Graphically you can see this by plotting your #cos#:
graph{cos(6x) [-3.895, 3.9, -1.95, 1.947]}

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