MHB 7.t.27 write eq for a sinusiol graph

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To write the equation for a sinusoidal graph with an amplitude of -3, a period of 2π/3, and a phase shift of -π/4, the standard form is y = A sin(ωx - φ) or y = A cos(ωx - φ). The amplitude is |A|, which is 3, and the period T is given as 2π/ω, allowing for the calculation of ω as 3. The phase shift φ can be determined using φ/ω, leading to φ being -π/4. The final equation for the sinusoidal graph is y = -3 sin(3x + π/4). Understanding these parameters is crucial for accurately representing sinusoidal functions.
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Write an equation for a sinusiol graph with the following
\quad $A=-3$ \quad period $=\dfrac{2\pi}{3}$ phase shift $=-\dfrac{\pi}{4}$
For the graphs of $y=A\sin(\omega x - \phi)$ or $y=A\cos(\omega x - \phi),\omega>0$
Amplitude $=|A|$ \quad Period $=T=\dfrac{2\pi}{\omega}$ \quad Phase shift $=\dfrac{\phi}{\omega}$
$y=-3\sin(\omega x - \phi)$

ok, I still get ? with these sinusol graphs
 
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You have the equations! Solve for [math]T = 2 \pi / 3[/math] so solve for [math]\omega[/math]. Then find [math]\phi[/math].

-Dan
 
topsquark said:
You have the equations! Solve for [math]T = 2 \pi / 3[/math] so solve for [math]\omega[/math]. Then find [math]\phi[/math].

-Dan

ok I think this is it ... typos maybe
$
Screenshot 2022-02-09 11.22.48 AM.png
 
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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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