What is the period of #y=8cos(5pix + (3pi)/2) - 9#?

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Answer 1 · 2016-07-09T12:54:10

#2/5#

The least positive value of T (if any) for which f(x+T) = f(x) is defined

as the period of f(x)

For sin x and cos x, the period is #2pi#.

For sin kx and cos kx, the period is #(2p)/k#.

For tan x, the period is #pi#.

For tan kx, the period is #pi/k#

Here, the form is #a sin (kx+b)+c=8 sin (5pix+(3pi)/2)-9.#.

The period is #(2pi)/k=(2pi)/(5pi)=2/5#. See how it works.

#y(x+2/5)=8 sin ((5pi(x+2/5)+(3pi)/2)-9#

#=8 sin (2pi+(5px+(3pi)/2))-9#

#=8 sin (5pix+(3pi)/2)-9#

#=y(x)#..