Finding c from graph

chocolate · July 2nd, 2012, 12:59 AM

Another one! Could get the answer for b this time, but not c.

The equation for this graph is acos(bx)+c

I got a and b this time, but not c, which is 7/2! How do I arrive at 7/2?

Thank you!

ZardoZ · July 2nd, 2012, 03:00 AM

[color=#000000] $y(x)=a\cdot \cos(b\cdot x)+c$
The range of values of y is the set [2,5], y is a periodic function so $a=5-\frac{5+2}{2}=5-3.5=1.5$ .

Now the period of y is ?, so $b\cdot \pi=2\pi\Rightarrow b=2$ and so $y(x)=\frac{3}{2}\cos(2x)+c$ .

$y\left(\frac{\pi}{2}\right)=2\Rightarrow \frac{3}{2}\cos\left(2\frac{\pi}{2}\right)+c=2\Rig htarrow c=2+\frac{3}{2}=\frac{7}{2}$ and

$y(x)=\frac{3}{2}\cos(2x)+\frac{7}{2}$ .[/color]

dibyendu · July 2nd, 2012, 03:02 AM

$y= a\;\cos(bx)\;+\;c$

Do you know the value of $y$ at $x= \frac{\pi}{2b}$ ?

This is the value of $c$

Best regards,

July 2nd, 2012, 03:00 AM	#2
ZardoZ Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus	Re: Finding c from graph [color=#000000] $y(x)=a\cdot \cos(b\cdot x)+c$ The range of values of y is the set [2,5], y is a periodic function so $a=5-\frac{5+2}{2}=5-3.5=1.5$ . Now the period of y is ?, so $b\cdot \pi=2\pi\Rightarrow b=2$ and so $y(x)=\frac{3}{2}\cos(2x)+c$ . $y\left(\frac{\pi}{2}\right)=2\Rightarrow \frac{3}{2}\cos\left(2\frac{\pi}{2}\right)+c=2\Rig htarrow c=2+\frac{3}{2}=\frac{7}{2}$ and $y(x)=\frac{3}{2}\cos(2x)+\frac{7}{2}$ .[/color]
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July 2nd, 2012, 03:02 AM	#3
dibyendu Senior Member Joined: Aug 2008 Posts: 113 Thanks: 0	Re: Finding c from graph $y= a\;\cos(bx)\;+\;c$ Do you know the value of $y$ at $x= \frac{\pi}{2b}$ ? This is the value of $c$ Best regards,
$dibyendu is offline$

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