How do you convert r 4sintheta to rectangular form?

How do you convert r 4sintheta to rectangular form?

1 Answer

1. r=4sinθ represents the circle of diameter 4 and center at #
2. For conversion to cartesian form, use sinθ=yr and.
3. r2=x2+y2 .
4. Substitutions give r=4(yr)
5. At the pole r=θ=0 , and so, x = y = 0. Elsewhere, cross-
6. multiplying, r2=x2+y2=4y .
7. In the standard form, this is x2+(y−2)2=22 .
8. r=2acos(θ−α) .

How do you convert spherical coordinates to rectangular coordinates?

Convert from spherical coordinates to rectangular coordinates

1. x=ρsinφcosθ
2. y=ρsinφsinθ
3. z=ρcosφ

How do you calculate r and theta?

To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

1. r = √ ( x2 + y2 )
2. θ = tan-1 ( y / x )

What is a rectangular form?

The rectangular form of a complex number is given by. z=a+bi . Substitute the values of a and b . z=a+bi =rcosθ+(rsinθ)i =r(cosθ+isinθ) In the case of a complex number, r represents the absolute value or modulus and the angle θ is called the argument of the complex number.

How do you convert polar equations to rectangular form?

To convert from polar coordinates to rectangular coordinates, use the formulas x=rcosθ and y=rsinθ.

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

r=−2sinθ=−yr . and so, r2=x2+y2=−2y .

What is Theta in spherical coordinates?

The coordinates used in spherical coordinates are rho, theta, and phi. Rho is the distance from the origin to the point. Theta is the same as the angle used in polar coordinates. Phi is the angle between the z-axis and the line connecting the origin and the point.

What is r Theta?

The Greek letter θ (theta) is often used to denote an angle, and a polar coordinate is conventionally referred to as (r, θ) instead of (x, y). They each take one argument, an angle measured in degrees.