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# Trig Function Graph

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I have two points. (-1,-5) is one of the minimum points and (3.5,-4) is one of the maximum points. I'm not sure if this is a sin or a cosine function. Please write the equation to this problem.

Sep 13, 2019

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.I literally just watched a video on how to do this, this is a learning process for me too

I am assuming that you learned the trig vocabulary for this as you asking these problems

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Lets first do a cosine graph cuz its easier

This is the base equation for a cosine graph:

$$y=A\cos{b}(x-h)+c$$

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So first find the amplitude, which is the height of the waves of the graph. (using y-values)

$$\text{Amplitude}=|\frac{\text{Max}-\text{Min}}{2}|$$

$$|\frac{-5-(-4)}{2}|$$

$$|\frac{-1}{2}|$$

$$\text{Amplitude}=\frac{1}{2}$$

Now we have the "A" value

$$y=\frac{1}{2}\cos{b}(x-h)+c$$

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Ok now we have to find the period

We first find the positive difference of the x values to find the horizontal distance.

$$|-1-3.5|=4.5$$

Then we double what we got

$$9$$

Then we solve for the b-value

$$9=\frac{2\pi}{b}\rightarrow9b=2pi\rightarrow{b}=\frac{2pi}{9}$$

Now we have

$$y=\frac{1}{2}\cos{\frac{2pi}{9}}(x-h)+c$$

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Now we have to find the phase shift (h-value)

Since it has shifted -1,                          ( coordinate (-1, -5) tells us that. )

We now have:

$$y=\frac{1}{2}\cos{\frac{2pi}{9}}(x+1)+c$$

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Now we have to find the vertical shift (c-value)

Formula for that is

$$c=\frac{\text{Maximum}}{2}$$

$$c=\frac{-5+(-4)}{2}$$

$$c=-4.5$$

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So the equation of the sinusoidal graph is

$$y=\frac{1}{2}\cos{\frac{2pi}{9}}(x+1)-4.5$$

This is the cosine graph.

This is the video I learned from, if you want to find the sine graph, follow the steps in the video.

Sep 14, 2019
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hellospeedmind  Sep 14, 2019
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CalculatorUser  Sep 14, 2019
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I was on Khan Academy. I typed in the answer, and it turns out that y=0.5cos((2π/9)​x−(7π/9​))−4.5 is the answer.

hellospeedmind  Sep 14, 2019
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did it tell you why the h-value was wrong?

CalculatorUser  Sep 14, 2019