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The graph of a sinusoidal function intersects its midline at
(0,-3) and then has a maximum point at
(2,-1.5).
Write the formula of the function, where
x is entered in radians.

f(x)=◻

The graph of a sinusoidal function intersects its midline at $(0,-3)$ and then has a maximum point at $(2,-1.5)$ . $\newline$ Write the formula of the function, where $x$ is entered in radians. $\newline$ $f(x)=\square$

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Evaluate piecewise-defined functions

Full solution

Q. The graph of a sinusoidal function intersects its midline at

(0,-3)

and then has a maximum point at

(2,-1.5)

.

\newline

Write the formula of the function, where

x

is entered in radians.

\newline

f(x)=\square

Solving for B: We know that $T = \frac{2\pi}{B}$ , so we can solve for B by rearranging the equation to $B = \frac{2\pi}{T}$ . $\newline$ $B = \frac{2\pi}{8}$ $\newline$ $B = \frac{\pi}{4}$
Plugging in the values: Let's plug in the values we have found into the formula: $\newline$ $f(x) = 1.5 \cdot \cos\left(\frac{\pi}{4} \cdot (x - 0)\right) - 3$

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