# Convert polar equation r= 1/1+sin(theta) to rectangular equation

• MHB
• Elissa89
In summary, the equation $r = \dfrac{1}{1+\sin{\theta}}$ can be simplified to $r = 1-y$ by dividing both sides by $r$ and then substituting $r+y$ with $1$.
Elissa89
The equation is:

r= 1/1+sin(theta)

I know the answer is supposed to be:

x^2+y^2=(1-y)^2

I can't figure out the steps to get to the answer.

Elissa89 said:
The equation is:

r= 1/1+sin(theta)

I know the answer is supposed to be:

x^2+y^2=(1-y)^2

I can't figure out the steps to get to the answer.

$r = \dfrac{1}{1+\sin{\theta}}$

divide both sides by $r$ ...

$1 = \dfrac{1}{r+r\sin{\theta}} \implies r+r\sin{\theta} = 1$

$r + y = 1$

$r = 1 - y$

can you finish?

skeeter said:
$r = \dfrac{1}{1+\sin{\theta}}$

divide both sides by $r$ ...

$1 = \dfrac{1}{r+r\sin{\theta}} \implies r+r\sin{\theta} = 1$

$r + y = 1$

$r = 1 - y$

can you finish?

Yes Thanks

## 1. How do you convert a polar equation to a rectangular equation?

To convert a polar equation to a rectangular equation, you can use the following formulas:x = r * cos(theta)y = r * sin(theta)Simply plug in the given values for r and theta into these equations to get the corresponding x and y values in rectangular form.

## 2. What is the significance of the polar equation r= 1/1+sin(theta)?

The polar equation r= 1/1+sin(theta) represents a cardioid, which is a heart-shaped curve. This curve is symmetrical about the origin and has a single petal. It is commonly used in mathematics and physics to model various phenomena.

## 3. How do you graph the polar equation r= 1/1+sin(theta)?

To graph the polar equation r= 1/1+sin(theta), you can plot points by choosing different values for theta and calculating the corresponding values for r. Then, connect these points to create the cardioid curve. Alternatively, you can use graphing software to plot the curve.

## 4. Can you simplify the polar equation r= 1/1+sin(theta) further?

Yes, the polar equation r= 1/1+sin(theta) can be simplified to r= cos(theta). This is because 1/1+sin(theta) is equivalent to cos(theta) due to the trigonometric identity: 1+sin^2(theta) = cos^2(theta). Therefore, the equation can also be written as r= cos(theta).

## 5. What is the rectangular equation equivalent of r= 1/1+sin(theta)?

The rectangular equation equivalent of r= 1/1+sin(theta) is (x^2 + y^2) - x = 0. This can be found by substituting the formulas for x and y in terms of r and theta into the polar equation, and then simplifying the resulting equation in terms of x and y.

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