Worksheet on Rectangular – Polar Conversion

In math worksheet on rectangular – polar conversion; students can practice the questions on how to convert rectangular coordinates to polar coordinates and also convert polar coordinates to rectangular coordinates (vice-versa).

Recall the formula from polar to rectangular:

To convert polar coordinates to rectangular coordinates;

x = r cos θ, y = r sin θ

Recall the formula from rectangular to polar:

To convert rectangular coordinates to polar coordinates; 

r = √(x² + y²) and tan θ = y/x or, θ = tan\(^{-1}\) y/x

To know more about the relation between the Cartesian co-ordinates and Polar co-ordinates and about more examples Click Here

Follow the above formula to solve the below questions given in the worksheet on rectangular – polar conversion. 

1. OX and OY are the cartesian axes of co-ordinates. Again 0 and OX are respectively the pole and initial line of a system of polar co-ordinates. With respect to these systems (i) if the polar co-ordinates of a point P be (2, 300), find the cartesian co-ordinates of the point; (ii) if the cartesian co-ordinates of a point P be (0, 2), find its polar co-ordinates. 

2. Find the Cartesian co-ordinates of the points whose polar co-ordinates are :

(i) (2, π/3)

(ii) (4, 3π/2)

(iii) (6, -π/6)

(iv) (-4, π/3)

(v) (1, √3).

3. Find the polar co-ordinates of the points whose Cartesian co-ordinates are:

(i) (2, 2).

(ii) (- √3, 1)

(iii) (- 1, 1)

(iv) (1, - 1)

(v) (-(5√3)/2, - 5/2).

4. Reduce each of the following Cartesian equations to polar forms:

(i) x² + y² = a²

(ii) y = x tan α

(iii) x cos α + y sin α = p

(iv) y² = 4x + 3

(v) x² - y² = a²

(vi) x² + y² = 2ax

(vii) (x² + y²)² = a²(x² - y²)

5. Transform each of the following polar equations to cartesian forms:

(i) r = 2a sin θ

(ii) l/r = A cos θ + B sin θ

(iii) r= a sin θ

(iv) r² = a²cos 2θ

(v) \(r^{\frac{1}{2}}\) \(a^{\frac{1}{2}}\) sin θ/2 

(vi) r² sin 2θ = 2a²

(vii) r cos (θ - α)

(viii) r(cos 3θ + sin 3θ) = 5k sin θ cos θ.

Answers for the worksheet on rectangular – polar conversion are given below to check the exact answers of the above questions.


1. (i) (√3 ,1)

(ii) (2, π/2);

2. (i) (1, √3)

(ii) (0, -4)

(iii) (3√3, -3)

(iv) (-2, -2√3),

(v) (cos √3, sin √3) where √3 is measured in radian.

3.(i) (2√2, π/4)

(ii) (2, 5π/6)

(iii) (√2, 3π/4)

(iv) (√2, -π/4)

(v) (5, 7π/6)

4. (i) r² = a²

(ii) θ = α

(iii) r cos (θ - α) = P

(iv) r² sin² θ = 4r cos θ + 3

(v) r² cos 2θ = a²

(vi) r = 2a cos θ

(vii) r² = a² cos 2θ.

5. (i) x² + y² = 2ay

(ii) Ax + By = l

(iii) x² + y² = ay

(iv) (x² + y²)² = a²(x² - y²)

(v) (2x² + 2y² + ax)² = a²(x² + y²)

(vi) xy = a²

(vii) x cos α + y sin α = p

(viii) x³ + 3x²y - 3xy² - y³ = 5kxy.

 Co-ordinate Geometry 

11 and 12 Grade Math 

From Worksheet on Rectangular – Polar Conversion to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheet on Triangle | Homework on Triangle | Different types|Answers

    Jun 21, 24 02:19 AM

    Find the Number of Triangles
    In the worksheet on triangle we will solve 12 different types of questions. 1. Take three non - collinear points L, M, N. Join LM, MN and NL. What figure do you get? Name: (a)The side opposite to ∠L…

    Read More

  2. Worksheet on Circle |Homework on Circle |Questions on Circle |Problems

    Jun 21, 24 01:59 AM

    In worksheet on circle we will solve 10 different types of question in circle. 1. The following figure shows a circle with centre O and some line segments drawn in it. Classify the line segments as ra…

    Read More

  3. Circle Math | Parts of a Circle | Terms Related to the Circle | Symbol

    Jun 21, 24 01:30 AM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  4. Circle | Interior and Exterior of a Circle | Radius|Problems on Circle

    Jun 21, 24 01:00 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More

  5. Quadrilateral Worksheet |Different Types of Questions in Quadrilateral

    Jun 19, 24 09:49 AM

    In math practice test on quadrilateral worksheet we will practice different types of questions in quadrilateral. Students can practice the questions of quadrilateral worksheet before the examinations

    Read More