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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
 #1
avatar+2552 
+3

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

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
 #2
avatar+333 
+3

I appreciate your answer. Thank you so much CalculatorUser!!!

hellospeedmind  Sep 14, 2019
 #3
avatar+2552 
+2

Your welcome!

CalculatorUser  Sep 14, 2019
 #4
avatar+333 
+2

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
 #5
avatar+2552 
+2

did it tell you why the h-value was wrong?

CalculatorUser  Sep 14, 2019

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