babeeb0oL

2021-08-22

Write an equation for a sinusoidal graph with the following properties:

$A=-3$ period $=\frac{2\pi}{3}$ phase shift $=-\frac{\pi}{4}$

rogreenhoxa8

Skilled2021-08-23Added 109 answers

Step 1

The general equation of sinusoidal equation is$y=A\mathrm{sin}(kx-\varphi )$ where A is the amplitude, C is the phase shift.

Equation the given period that is$\frac{2\pi}{3}$ to $\frac{2\pi}{k}$ to obtain the value of k.

$\frac{2\pi}{3}=\frac{2\pi}{k}$

$k=3$

Step 2

Equate the given phase shift to$\frac{\varphi}{k}$ and Substitute 3 for k in $-\frac{\pi}{4}=\frac{\varphi}{k}$ to obtain the value of $\varphi$

$-\frac{\pi}{4}=\frac{\varphi}{3}$

$\varphi =-\frac{3\pi}{4}$

Substitute the obtained values of$A,\text{}k,\text{}\varphi$ in $y=A\mathrm{sin}(kx-\varphi )$ and simplify to obtain the equation of sinusoidal equation.

$y=A\mathrm{sin}(kx-\varphi )$

$y=-3\mathrm{sin}(3x-(-\frac{3\pi}{4}))$

$=-3\mathrm{sin}(3x+\frac{3\pi}{4})$

The general equation of sinusoidal equation is

Equation the given period that is

Step 2

Equate the given phase shift to

Substitute the obtained values of

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