Question

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)=

Answer 1

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

Explanation:

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