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)=
1 answer:
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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