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clara1223
 one year ago
simplify the following, where k represents any integer: cos(2kpix)(sin(2kpix))
a) cosx*sinx
b) (1/2)sin(2x)
c) cos((1/2)x)^2
d) cos(x)^2*sin(x)^2
e) undefined
clara1223
 one year ago
simplify the following, where k represents any integer: cos(2kpix)(sin(2kpix)) a) cosx*sinx b) (1/2)sin(2x) c) cos((1/2)x)^2 d) cos(x)^2*sin(x)^2 e) undefined

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clara1223
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 could you explain how you got that answer please?

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.2https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Symmetry.2C_shifts.2C_and_periodicity https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Doubleangle.2C_tripleangle.2C_and_halfangle_formulae

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Here is the explanation: Since the sine and cosine are periodic functions with a period of 2pi, sin (2kpi  x) = sin (x) and cos(2kpi  x) = cos (x) Ok so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Then because of even and odd functions, sin (x) =  sin x and cos (x) = cos x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Putting it all together, you get: \((\cos (2k \pix)) ((\sin(2k \pix)) \) \(= \cos (x) \sin (x)\) \(=  \sin x \cos x\)

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 thanks so much!

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.2wait ...... sin(x) = sin(x) it equals positive sin(x) cos(x) then use double angle identity for sin > sin(2x) = 2sincos > sincos = 1/2 sin(2x)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0@dumbcow You're correct. I missed the negative with the sin in the original problem.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0This is how it should read: \((\cos (2k \pix)) ((\sin(2k \pix))\) \(= \cos (x)( \sin (x))\) \(= \cos x ((\sin x))\)\) \(= \sin x \cos x\) \(=\dfrac{1}{2} \sin 2x\)
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