What is the standard form of the equation in rectangular form R 9?

Note that this should make sense intuitively, as r=9 in polar coordinates is all points of distance 9 from the origin, that is, a circle of radius 9 centered at the origin, and the formula for a circle of radius s centered at (h,k) in Cartesian coordinates is (x−h)2+(y−k)2=s2 .

Is R 3 a polar equation?

Explanation: it’s already in polar form.

In what axis does the polar equation r sin symmetric?

x -axis
r = 2 sin ⁡ This equation exhibits symmetry with respect to the line θ = π 2 \displaystyle \theta =\frac{\pi }{2} θ=2π​. In the second test, we consider symmetry with respect to the polar axis ( x -axis).

What is a rectangular equation?

A rectangular equation, or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane. For example y=4x+3 is a rectangular equation. These equations may or may not be graphed on Cartesian plane.

What is r in rectangular?

When we think about plotting points in the plane, we usually think of rectangular coordinates (x,y) in the Cartesian coordinate plane. The first coordinate r is the radius or length of the directed line segment from the pole. The angle θ, measured in radians, indicates the direction of r.

Why is a cardioid called a cardioid?

A cardioid (from the Greek καρδία “heart”) is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. Named for its heart-like form, it is shaped more like the outline of the cross section of a round apple without the stalk.

What is the rectangular form of R − 2 sin θ )?

r=−2sinθ=−yr . and so, r2=x2+y2=−2y .

How do you convert R = 4 1 – cos to rectangular form?

How do you convert r = 4 1 − cos θ to rectangular form? Multiply both sides by (1 − cosθ) to get: We could express this equation in other ways, but note that √x2 + y2 is the non-negative square root. So if our reexpression involves eliminating the square root by squaring then we need the restriction x ≥ −4.

How do you convert exponential forms to rectangular forms?

Exponential forms of numbers can be converted into their rectangular equivalents by the following formulas. The real value (the x value) of the rectangular form can be obtained through the formula, x= r cos (θ).

How do you find the real value of a rectangular form?

The x is the real number of the expression and the y represents the imaginary number of the expression. Exponential forms of numbers can be converted into their rectangular equivalents by the following formulas. The real value (the x value) of the rectangular form can be obtained through the formula, x= r cos (θ).

What is the difference between complex exponential numbers & rectangular numbers?

Unlike the polar form, which is expressed in unit degrees, a complex exponential number is expressed in unit radians. Rectangular forms of numbers take on the format, rectangular number= x + jy, where x and y are numbers. The x is the real number of the expression and the y represents the imaginary number of the expression.