How do you find the period of #y = -10cos((pi x)/6)#?

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Answer 1 · 2016-10-15T01:55:23

The period is 12.

#y=-10cos(color(red)(pi/6)x)#

The general form of a cosine equation is

#y=Acos(color(red)Bx-C)+D# where

#A=# amplitude

#(2pi)/color(red)B=# the period

#C/B=# the phase shift

#D=# the vertical shift

In our example, #color(red)B=color(red)(pi/6)# and

the period #=frac{2pi}{color(red)B}=frac{2pi}{color(red)(pi/6)}=2pi*6/pi=12#