What are the x-intercepts of #f(x) =30sin(3x)cos(3x)#?

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Answer 1 · 2018-02-06T21:31:27

#x= pi/3n or pi/6 + pi/3n#

We can quickly see that

#f(x) = 15(2sin(3x)cos(3x))#

Letting #u = 3x#, then

#f(x) = 15(2sinucosu)#

#f(x) = 15sin(2u)#

#f(x) = 15sin(6x)#

This will have zeroes when

#0 = 15sin(6x)#

#sin(6x) = 0#

#6x = 0 or pi#

#x = 0 or x = pi/6#

The period of #sin(6x)# is #(2pi)/6 = pi/3#, thus,

#x = pi/3n or pi/6 + pi/3n#

I will leave finding the solution values in the required domain as an exercise.

Hopefully this helps!