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jok3333 [9.3K]
2 years ago
11

Ff is a trigonometric function of the form f(x)=a\sin(bx+c)+df(x)=asin(bx+c)+df, left parenthesis, x, right parenthesis, equals,

a, sine, left parenthesis, b, x, plus, c, right parenthesis, plus, d.
Below is the graph f(x)f(x)f, left parenthesis, x, right parenthesis. The function intersects its midline at (3,-6.5)(3,−6.5)left parenthesis, 3, comma, minus, 6, point, 5, right parenthesis and has a maximum point at (4,-2)(4,−2)left parenthesis, 4, comma, minus, 2, right parenthesis.
Find a formula for f(x)f(x)f, left parenthesis, x, right parenthesis. Give an exact expression.
\qquad f(x)=f(x)=f, left parenthesis, x, right parenthesis, equals
\qquad

Mathematics
1 answer:
andriy [413]2 years ago
3 0

The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

<h3>How to derive a sinusoidal expression</h3>

In this problem we need to find a <em>sinusoidal</em> expression that models the curve seen in the picture. The most typical <em>sinusoidal</em> model is described below:

f(x) = a · sin (b · x + c) + d    (1)

Where:

  • a - Amplitude
  • b - Angular frequency
  • c - Angular phase
  • d - Vertical midpoint

Now we proceed to find the value of each variable:

Amplitude

a = - 2 - (-6.5)

a = 4.5

Angular frequency

b = 2π / T, where T is the period.

0.25 · T = 4 - 3

T = 4

b = 2π / 4

b = π / 2

Midpoint

d = - 6.5

Angular phase

- 2 = 4.5 · sin (π · 4/2 + c) - 6.5

4.5 = 4.5 · sin (π · 4/2 + c)

1 = sin (2π + c)

π = 2π + c

c = - π

The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

To learn more on trigonometric functions: brainly.com/question/15706158

#SPJ1

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