Saylilbaby
  • Saylilbaby
which cosine function has maximum of 4, a minimum of -4, and a period of 2pie/3?
Mathematics
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chestercat
  • chestercat
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Saylilbaby
  • Saylilbaby
@dan815 @hartnn @idku
boldjon
  • boldjon
period of cos x is 2π period of cos (ax) is 2π/a because cos (a(x + 2π/a) ) = cos (ax + 2π) = cos (ax) if we need period 2π/3 the function must be cos (3x) furthermore, as - 1 ≤ cos x ≤ 1 it will be - 2 ≤ 2 cos x ≤ 2 putting together the two things, the answer is c) y = 2 cos (3θ)
boldjon
  • boldjon
de nada (¬‿¬)

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mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
BTW, \(y = \cos \theta\), for any value of \(\theta\), has a maximum of 1 and a minimum of -1. To have a maximum of 4 and a minimum of -4, you need to have \(y=4\cos \theta\) Now you need to adjust \(\theta\) to have a period of \(\dfrac{2 \pi}{3}\)

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