## Polar to Cartesian Equation Calculator

## FAQs

**How do you convert a polar equation to Cartesian?** To convert a polar equation to Cartesian form, you use the following trigonometric relationships: x = r * cos(θ) y = r * sin(θ) where ‘r’ is the radius and ‘θ’ is the angle in radians.

**How to convert a polar equation to a rectangular equation calculator?** To create a calculator for converting polar equations to rectangular equations, you can use HTML, CSS, and JavaScript code to take input for ‘r’ and ‘θ’ and then apply the trigonometric formulas to calculate ‘x’ and ‘y’ (Cartesian coordinates). You can find a sample code in the previous answer.

**How do you convert complex numbers to Cartesian form?** To convert a complex number from polar form (r∠θ) to Cartesian form (a + bi), use the following formulas: a = r * cos(θ) b = r * sin(θ)

**How to convert from polar coordinates to rectangular coordinates?** To convert from polar coordinates (r, θ) to rectangular coordinates (x, y), use the trigonometric formulas mentioned above: x = r * cos(θ) y = r * sin(θ)

**How do you convert polar to Cartesian in Excel?** In Excel, if you have the polar coordinates (radius ‘r’ in cell A1 and angle ‘θ’ in cell A2), you can use the following formulas to convert to Cartesian coordinates (x and y): In cell B1: =A1 * COS(A2) In cell B2: =A1 * SIN(A2) Cell B1 will contain the x-coordinate, and cell B2 will contain the y-coordinate.

**Can we convert polar form back into rectangular form?** Yes, you can convert a complex number in polar form (r∠θ) back to rectangular form (a + bi) using the formulas mentioned above.

**How do you find the Cartesian equation?** To find the Cartesian equation of a curve given in polar form, use the conversion formulas: x = r * cos(θ) and y = r * sin(θ). Then express ‘r’ in terms of ‘x’ and ‘y’ to get the Cartesian equation.

**How to convert from polar form to rectangular form complex numbers?** To convert a complex number from polar form (r∠θ) to rectangular form (a + bi), use the formulas: a = r * cos(θ) and b = r * sin(θ).

**What is the difference between polar form and Cartesian form?** Polar form uses radius ‘r’ and angle ‘θ’ to represent a point, while Cartesian form (rectangular form) uses ‘x’ and ‘y’ coordinates to represent a point. Polar form is often used to represent complex numbers, while Cartesian form is commonly used in standard coordinate systems.

**How do you write something in Cartesian form?** To write a point or equation in Cartesian form, express it using ‘x’ and ‘y’ coordinates without any trigonometric functions or polar terms.

**What is the relationship between polar and Cartesian coordinates?** The relationship between polar and Cartesian coordinates is given by the formulas: x = r * cos(θ) and y = r * sin(θ). Polar coordinates (r, θ) represent a point’s distance and angle from the origin, while Cartesian coordinates (x, y) represent the point’s location on the XY-plane.

**What is the formula for polar coordinates?** Polar coordinates are represented as (r, θ), where ‘r’ is the radial distance from the origin, and ‘θ’ is the angle (in radians) from the positive x-axis.

**Are Cartesian and rectangular coordinates the same?** Yes, Cartesian coordinates and rectangular coordinates are often used interchangeably. Both refer to the same coordinate system using ‘x’ and ‘y’ axes.

**What is R in polar coordinates?** In polar coordinates, ‘r’ represents the radial distance or the distance from the origin to a point.

**How do you convert polar to rectangular in Matlab?** In Matlab, if you have ‘r’ and ‘θ’ as variables, you can use the following code to convert to Cartesian coordinates:

`matlabCopy code````
x = r * cos(theta);
y = r * sin(theta);
```

**How to turn rectangular form into polar form to exponential form?** To convert a complex number from rectangular form (a + bi) to polar form (r∠θ), you can use the following formulas: r = √(a^2 + b^2) θ = atan2(b, a) To convert to exponential form (re^iθ), use Euler’s formula: e^(iθ) = cos(θ) + i*sin(θ).

**What is an example of a Cartesian coordinates equation?** An example of a Cartesian coordinates equation is the equation of a line: y = mx + b, where ‘m’ is the slope and ‘b’ is the y-intercept.

**How do you find the Cartesian equation with two points?** To find the equation of a line in Cartesian coordinates given two points (x1, y1) and (x2, y2), use the point-slope form: y – y1 = m(x – x1), where ‘m’ is the slope calculated as (y2 – y1) / (x2 – x1).

**What is a Cartesian equation example?** An example of a Cartesian equation is the equation of a circle with radius ‘r’ and center at (h, k): (x – h)^2 + (y – k)^2 = r^2.

**How do you change from polar form?** To change from polar form to rectangular form, use the formulas: x = r * cos(θ) and y = r * sin(θ) for each point (r, θ) in the polar coordinates.

**How do you graph a polar equation?** To graph a polar equation, plot points corresponding to different values of ‘r’ and ‘θ’ and connect them to form the curve. You can use software like Matlab, Python, or graphing calculators for precise graphs.

**How do you convert a given vector in polar form to rectangular form?** To convert a vector from polar form (magnitude ‘r’ and angle ‘θ’) to rectangular form (components ‘x’ and ‘y’), use the formulas: x = r * cos(θ) and y = r * sin(θ).

**How do you change a Cartesian integral to a polar integral?** To change a Cartesian integral to a polar integral, substitute ‘x’ and ‘y’ with their polar equivalents using the conversion formulas.

**How do you turn a complex number into a real number?** A complex number cannot be turned into a real number, as a real number has no imaginary component. However, you can extract the real part of a complex number by taking its real component.

**How do you convert rectangular to polar without a calculator?** To convert a complex number from rectangular form (a + bi) to polar form (r∠θ) without a calculator, calculate ‘r’ using √(a^2 + b^2) and ‘θ’ using atan2(b, a).

**How do you convert Cartesian coordinates to polar or cylindrical?** To convert Cartesian coordinates (x, y, z) to polar or cylindrical coordinates, use the following formulas: r = √(x^2 + y^2) θ = atan2(y, x) z remains unchanged.

**How do you find the polar coordinate between two points?** To find the polar coordinate between two points (x1, y1) and (x2, y2), calculate the distance ‘r’ between the points using √((x2 – x1)^2 + (y2 – y1)^2) and the angle ‘θ’ using atan2(y2 – y1, x2 – x1). The polar coordinates will be (r, θ).

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