Equation of the function: f(x) = 4 sin (x/2) + 6.
What is sinusoidal function ?
The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).
Given: max value= 6, min value= -2, y-intercept= 6.
As, standard form f(x) = A sin (ωx +φ) + k,
where A is the amplitude, ω is the angular velocity with ω=2πf.
Now,
A = |6- (-2)/2|
A = |6 +2/2| = 8/2
A = 4
Also, ω:
The period of a sinusoidal is T = 1/f
so, f = 1 / T
ω = 2πf
ω = 2π ( 1/T) with T = 4π
ω = 2π (1/(4π) = 2π (2)
ω = 1/2
The y-intercept k = 6
So, equation with values A =4, ω = 1/2, k = 6, φ = 0.
f(x) = A f(x)
f(x) = A sin (ωx +φ) + k
f(x) = 4 sin (x/2) + 6.
Hence, equation of the function f(x) = 4 sin (x/2) + 6.
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