Perpendicular distance to the y-axis

Abcissa = |5| =

Perpendicular distance to the x-axis

Ordinate = |30| =

Since our x coordinate of 5 is positive

We move up on the graph 5 space(s)

Since our y coordinate of 30 is positive

We move right on the graph 30 space(s)

(5,30) is in Quadrant I

Convert the point (5,30°) from

polar to Cartesian

Cartesian Coordinates are (x,y)

Polar to Cartesian Transformation is

(r,θ) → (x,y) = (rcosθ,rsinθ)

(r,θ) = (5,30°)

(rcosθ,rsinθ) = (5cos(30),5sin(30))

(rcosθ,rsinθ) = (5(0.86602540408359),5(0.49999999948186))

(rcosθ,rsinθ) =

(5,30°) =

(4.3301,2.5) is in Quadrant I

Convert (5,30) to polar

Cartesian Coordinates are denoted as (x,y)

Polar Coordinates are denoted as (r,θ)

(x,y) = (5,30)

r = ±√5

r = ±√25 + 900

r = ±√925

r =

θ = tan

θ = tan

θ

Angle in Degrees = | Angle in Radians * 180 |

π |

θ_{degrees} = | 1.4056476493803 * 180 |

π |

θ_{degrees} = | 253.01657688845 |

π |

θ

Therefore, (5,30) =

(5,30) is in Quadrant I

(5,30° + 360°)

(5,390°)

(5,30° + 360°)

(5,750°)

(5,30° + 360°)

(5,1110°)

(-5,210°)

(-5,-150°)

then the point (-x,-y) is also on the graph

(-5, -30)

then the point (x, -y) is also on the graph

(5, -30)

then the point (-x, y) is also on the graph

(-5, 30)

Take (5, 30) and rotate 90 degrees

We call this R

The formula for rotating a point 90° is:

R

R

R

Take (5, 30) and rotate 180 degrees

We call this R

The formula for rotating a point 180° is:

R

R

R

Take (5, 30) and rotate 270 degrees

We call this R

The formula for rotating a point 270° is:

R

R

R

Take (5, 30) and reflect over the origin

We call this r

Formula for reflecting over the origin is:

r

r

r

Take (5, 30) and reflect over the y-axis

We call this r

Formula for reflecting over the y-axis is:

r

r

r

Take (5, 30) and reflect over the x-axis

We call this r

Formula for reflecting over the x-axis is:

r

r

r

Abcissa = |5| = **5**

Ordinate = |30| =**30**

Quadrant = I

Quadrant = I

r =**±30.413812651491**

θ_{radians} = 1.4056476493803

(5,30) =**(30.413812651491,80.54°)**

Quadrant = I

Ordinate = |30| =

Quadrant = I

Quadrant = I

r =

θ

(5,30) =

Quadrant = I

CCSS.MATH.CONTENT.6.NS.C.6.B

Free Ordered Pair Calculator - This calculator handles the following conversions:

* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

This calculator has 1 input.

* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

This calculator has 1 input.

Cartesian Coordinate = (x, y)

(r,θ) → (x,y) = (rcosθ,rsinθ)

For more math formulas, check out our Formula Dossier

(r,θ) → (x,y) = (rcosθ,rsinθ)

For more math formulas, check out our Formula Dossier

- cartesian
- a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length
- coordinates
- A set of values that show an exact position
- cos
- cos(θ) is the ratio of the adjacent side of angle θ to the hypotenuse
- degree
- A unit of angle measurement, or a unit of temperature measurement
- ordered pair
- A pair of numbers signifying the location of a point

(x, y) - point
- an exact location in the space, and has no length, width, or thickness
- polar
- a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction
- quadrant
- 1 of 4 sections on the Cartesian graph. Quadrant I: (x, y), Quadrant II (-x, y), Quadrant III, (-x, -y), Quadrant IV (x, -y)
- quadrant
- 1 of 4 sections on the Cartesian graph. Quadrant I: (x, y), Quadrant II (-x, y), Quadrant III, (-x, -y), Quadrant IV (x, -y)
- rectangular
- A 4-sided flat shape with straight sides where all interior angles are right angles (90°).
- reflect
- a flip creating a mirror image of the shape
- rotate
- a motion of a certain space that preserves at least one point.
- sin
- sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
- x-axis
- the horizontal plane in a Cartesian coordinate system
- y-axis
- the vertical plane in a Cartesian coordinate system

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