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Irina18 [472]
3 years ago
6

The graph of a sinusoidal function has a maximum point at (0,10) and then intersects its midline at (pi/4,4). Write the formula

of the function, where x is entered in radians. f(x)=
Mathematics
1 answer:
docker41 [41]3 years ago
5 0

Answer: y = 6 cos (2x) + 4

<u>Step-by-step explanation:</u>

A cosine function is expressed as: y = A cos (Bx - C) + D   where

  • amplitude (A) is the distance from the midline to the max/min.
  • B = 2π/P  where P is the period
  • C/B is the phase shift
  • D is the center line (aka midline)

A = Max - Midline

   = 10 - 4

   = 6

The max to the midpoint is π/4

⇒ 1/4 P = π/4

⇒ P = π

B = 2π/P    

  = 2π/π

  = 2

C = 0 because there is no phase shift

D = 4 (given)

Input A = 6, B = 2, C = 0, and D = 4 into the cosine function:

y = 2 cos (2x - 0) + 4

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