# Precalculus : Determine the Polar Equation of a Graph

## Example Questions

### Example Question #1 : Determine The Polar Equation Of A Graph

Which polar equation would produce this graph?

Possible Answers:

Correct answer:

Explanation:

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 , so the first number must be 2. Since vertically the graph goes from 0 to 4, the second number must be 2, because and .

### Example Question #2 : Determine The Polar Equation Of A Graph

Give the polar equation for this graph:

Possible Answers:

Correct answer:

Explanation:

This graph shows a rose curve with an odd number of petals.

This means that the equation will be in the form , where represents the length of the "petals" and represents the number of petals.

There are 5 petals of length 7.

### Example Question #1 : Graphs Of Polar Equations

Which polar equation would produce this graph?

Possible Answers:

Correct answer:

Explanation:

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 where is the length of each petal, and is half the number of petals. (Note that for an odd number of petals, the rose curve will have exactly petals). In this case, the petals have length 5, and there are 8 of them [half of 8 is 4].

### 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:

Possible Answers:

Correct answer:

Explanation:

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  because .

Thus our answer is,

.

### Example Question #5 : Determine The Polar Equation Of A Graph

Which of the following polar equations would produce this graph?

Possible Answers:

Correct answer:

Explanation:

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  should add to 2, making the correct choice .