Finding Max & Min of r=2-2cos(\Theta)

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In summary, the equation for finding the maximum and minimum values of r is r = 2 - 2cos(\Theta), where r represents the distance from the origin and \Theta represents the angle in radians. To find these values, the trigonometric identity cos(\Theta) = 1 and cos(\Theta) = -1 can be used. The graph of this equation is a cardioid, which is a heart-shaped curve with a single loop. Finding the maximum and minimum values of r is significant because it can help determine the range of possible distances from the origin for a given angle, which has practical applications in various fields such as physics, engineering, and astronomy.
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Ashford
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Homework Statement


Find the Maximum and Minimum of the following equation.
r=2-2cos([tex]\Theta[/tex])


The Attempt at a Solution


Max- 2-2 cos (0[tex]\pi[/tex])=0
(0,0[tex]\pi[/tex]);(0,2[tex]\pi[/tex])

Min 2-2cos([tex]\pi[/tex])=4
(4,[tex]\pi[/tex])

Do i just have these backwards?
 
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  • #2
0<4, so yes, you have them backwards. 4 is the max, 0 is the min.
 
  • #3
I'm wondering how you determined that
Max- 2-2 cos (0)=0
(0,0[itex]\pi[/itex\);(0,2[itex]\pi[/itex])

Min 2-2cos()=4
(4,[itex]\pi[/itex])

And, by the way, an equation does not have a max or min- a function does. An equation does not even have a "value" to be max or min.
 

1. What is the equation for "Finding Max & Min of r=2-2cos(\Theta)"?

The equation is r = 2 - 2cos(\Theta), where r represents the distance from the origin and \Theta represents the angle in radians.

2. How do you find the maximum and minimum values of r?

To find the maximum and minimum values of r, you can use the trigonometric identity cos(\Theta) = 1 when \Theta = 0 and cos(\Theta) = -1 when \Theta = \pi. Substituting these values into the equation r = 2 - 2cos(\Theta), we get the maximum value of r as 4 and the minimum value as 0.

3. What does the graph of r = 2 - 2cos(\Theta) look like?

The graph of this equation is a cardioid, which is a heart-shaped curve. It has a single loop and is symmetric about the x-axis.

4. What is the significance of finding the maximum and minimum values of r?

Finding the maximum and minimum values of r can help determine the range of possible distances from the origin for a given angle. This can be useful in various applications such as calculating the trajectory of a projectile or determining the shape of a rotating object.

5. Can this equation be applied in real-world situations?

Yes, this equation can be applied in various real-world situations such as in physics, engineering, and astronomy. It is commonly used to describe the motion of objects in circular or elliptical paths.

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