Precalculus : Graphs of Polar Equations
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Example Questions
Example Question #1 : Determine The Polar Equation Of A Graph
Which polar equation would produce this graph?
This is the graph of a cardiod. Based on its orientation where the cusp [pointy part] is on the y-axis, it is a sine and not cosine function. The x-intercepts are at 
Example Question #2 : Determine The Polar Equation Of A Graph
Give the polar equation for this graph:
This graph shows a rose curve with an odd number of petals.
This means that the equation will be in the form 
There are 5 petals of length 7.
Example Question #1 : Graphs Of Polar Equations
Which polar equation would produce this graph?
This graph shows a rose curve with an even number of petals. The first petal also intersects with the x-axis. This means that the equation will be in the form 
Example Question #1 : Determine The Polar Equation Of A Graph
Please choose the best answer from the following choices.
Determine the equation of the following polar graph:
Each loop is on the line of each axis, which means the equation will have a cosine.
The loops stretch out to the third unit on each axis, which means there will be a three in front of the cosine.
Lastly, there are 4 loops. Whenever there is an even number of loops, you divide that number by 2, and that is the number which goes in front of theta in the parentheses. In this case, it is 
Thus our answer is,
Example Question #5 : Determine The Polar Equation Of A Graph
Which of the following polar equations would produce this graph?
You can tell from the direction of the cardioid, extending horizontally, that you are dealing with a cosine graph. Then you should note that the y-intercepts are at 1 and -1, telling you that the first number must be 1. And since the graph extends to x = 2, you should note that the two numeric terms in 
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