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.
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?
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.
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.
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.
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).
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.